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Architecture and Mathematics in Ancient Egypt
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  • 102 b/w illus. 9 tables
  • Page extent: 304 pages
  • Size: 247 x 174 mm
  • Weight: 0.75 kg

Library of Congress

  • Dewey number: 722/.2
  • Dewey version: 21
  • LC Classification: NA215 .R67 2004
  • LC Subject headings:
    • Architecture, Ancient--Egypt
    • Architecture--Egypt--Mathematics
    • Pyramids--Egypt

Library of Congress Record

Hardback

 (ISBN-13: 9780521829540 | ISBN-10: 0521829542)




Index




Aamaket, tomb of 232

Abd el-Latyf 70

Abu Rawash 193, 225, 245

Abusir 61, 181, 183, 206, 207, 230, 231, 247

Abydos 30, 180, 181, 183, 232, 234

Agrigentum, temple of the Concord at 13

Ahmose (Eighteenth Dynasty) xxi, 181, 232

Akhenaten (Amenhotep IV, Eighteenth Dynasty) xxi, 99, 129

Alberti, Leon Battista 3

Alexander the Great xxi, 172

Alexandria 68

algorithm 58

Amada 105

Amarna 47, 73, 99, 101, 105, 127, 129, 153, 155

   Royal Tomb 83–84, 141

   period xxi, 104

Amduat 141

Amenemhat I (Twelfth Dynasty) xxi, 203, 229, 230, 251

Amenemhat II (Twelfth Dynasty) xxi, 229, 252

Amenemhat III (Twelfth Dynasty) xxi, 104, 115, 135, 138, 174, 183, 194, 206, 230, 253–254

Amenemhat IV (Twelfth Dynasty) xxi

Amenemhat-Serer, statue of 154

Amenhotep III (Eighteenth Dynasty) xxi, 115, 135–138, 150, 174, 205, 212

Amenhotep IV (Akhenaten, Eighteenth Dynasty) xxi

Amenhotepsesi, tomb of 154

Amenmesse (Nineteenth Dynasty) 142, 144

Ameny Qemau (Thirteenth Dynasty) xxi, 230, 254

amulets 70–71

Aniba 181, 233

angle 2, 43, 71, 196–197

   angle contraction 175

   right angle 22, 88, 122, 157, 158

Antony 172

apothem 200, 203, 207–211

approximation 10, 15, 26, 35, 54, 60, 66, 67, 70, 87, 112, 175, 212–213, 214, 228

apron 69

arches

   at St Chamas in Provence 13

   of Titus in Rome 13

Archimedes 66–67, 215, 240

architectural drawings (see also drawings and geometrical drawings) xv, 10, 60, 83, 90, 101, 113, 124, 127–128, 129, 139, 140, 141, 166, 174, 240

   of a building from Lisht 104

   of a building from the Ramesseum 104

   of a building from the Sheikh Said quarry 104, 105

   of a capital from Gebel Abu Foda 113, 117–121

   of a capital from the temple of Kalabsha 113

   of a cavetto cornice from the temple of Edfu 113

   of a colonnaded court from Dra Abu el-Naga 104

   of a column from the Temple of Philae 113, 117–121, 127, 167

   of a curve with coordinates from Saqqara 104, 115

   of an elliptical vault from the tomb of Ramses VI 113, 114–115, 157, 158, 159, 218

   of a four-pillared chamber of a tomb 104, 105–109, 144, 147

   of a garden or temple from Deir el-Bahari 104

   of a Hathor-headed capital from Gebel Abu Foda 113, 122, 167

   of a house 104

   of a house from Amarna 104

   of a peripteral chapel (?) on a wooden board 104, 109–112

   of a peripteral chapel from Deir el-Bahari 104, 105, 107, 111

   of pyramids 14 and 15 at Soleb 104, 186

   of a pyramid from Meroe 104, 186

   of a shrine: see of a peripteral chapel from Deir el-Bahari

   of the sloping sides of Mastaba 17 at Meidum 113, 114, 188–192

   of the stairs and door of a tomb 104

   of a temple at Heliopolis 100–101, 104

   of a tomb, from the tomb of Senenmut 104, 105–109

   of the tomb of Ramses IV 104, 112

   of the tomb of Ramses IX 104, 112

   vertical section of pyramid Beg. 8 at Meroe 104, 192, 234

architectural models xv, 90, 127–128, 138, 174, 175, 192, 194–195

   of columns and capitals 135–138

   of a granary 128

   of a house 128

   of the funerary apartment of a pyramid from Dahshur 128, 135–138, 175

   of the pyramid of Hawara(?) 128, 135–138, 194

   of a step pyramid 128, 131–133, 135, 194

   of a temple of Seti I 128, 129–131

   of the temple of Tôd 128, 129, 131–133

   from the tomb of Meketra 128

   of a T-shaped basin from Amarna 128

   votive 129, 131, 133, 135, 138

architecture 2, 4, 5, 10, 61, 87, 88, 122, 240

   Achaemenid 16

   Egyptian xv, xvi, 5, 6, 7, 10, 16, 28, 31, 46, 57, 69, 85, 86, 87, 127, 138, 155, 162, 173, 176, 180, 182, 226, 239

   Greek 7, 10, 90, 127, 173, 176

   Minoan 79

   relationship with mathematics xiv–xv, 2

   Roman 90, 176

archive 100

area of the circle 215

Arsenal inscription 175

art 2, 4, 5, 226

   Egyptian 2, 10, 31, 57, 85, 86, 96, 154–155

   Greek 7, 10

Ashmunein 85

Atmu-neferu, Queen of Senusret II (Twelfth Dynasty) 212, 252

Augustus xxi, 167, 172

axis 42, 43, 71, 122, 133, 153, 166, 187, 192, 207, 211

basalt 206, 207, 230

Basilica of Constantine 11–13

Belzoni, Giovanni 239

benben stone 182, 185, 198

benbenet (see also capstone and pyramidion) 182–183, 184

Beni Hasan 4

Bent Pyramid: see pyramids

Bryson 66

Building Texts 85, 117, 159, 161–172

burial chamber of a tomb (see also ‘house of gold’ and ‘hall’) 140

Byzantine division table 121

Byzantine Period xxi

Cagliostro 239

Cairo Calendar: see Papyrus Cairo 86637

Calendars of Lucky and Unlucky Days 80–81

capital 2, 18–43

   sketch from Gebel Abu Foda 113, 117–121

   sketch from the temple of Kalabsha 113

   sketch of a Hathor-headed from Gebel Abu Foda 113, 122, 167

capstone (see also pyramidion) 138, 182, 184, 207, 208, 211

cathedrals

   Amiens 13

   Notre-Dame de Paris 13

catheti 4, 28, 67, 185, 192, 203

cavetto cornice 113

cenotaph 135, 181, 232, 243, 244

chapel (see also peripteral chapels)

   of Hakoris at Karnak 54, 124

   of Ti 5

Chefren: see Khafra

Cheops: see Khufu

circle 5, 11, 32, 65, 66, 90, 115, 200

   calculation of the area 60

      Greek method 66–67

      Egyptian method 65–67

circumference 65, 66–67, 115, 200, 201

Clemens of Alexandria 156–157

Cleopatra VII xxi, 172

Colonna, Francesco 239

columns 2, 15, 18–43, 96, 97, 101, 114, 127, 132–133, 226

   drawing from the Temple of Philae 113, 117–121, 127, 167

cords (see also ropes) 61, 71, 115, 152, 153, 154–159, 216

      ‘stretching the cord’: see foundation ceremonies

corridors

   of pyramids 197, 224

   of tombs 84, 140, 142

   slope of 141, 142, 218

Corinth, temple of 13

Concord at Agrigentum, temple of 13

Crete 79

cubit (unit of measurement) 54, 59–60, 61, 85, 88, 109, 111, 112, 115, 117, 121, 122–123, 124, 127, 129, 142–147, 154, 155, 159, 166, 167, 171, 185, 188, 191, 192, 197, 202, 208, 212, 213–214, 218, 219, 226, 228, 229, 233, 234, 236, 242–254

   small cubit 59, 61, 129, 226

   royal cubit 59, 61, 129, 141, 201

   cubit rod 61, 88, 112, 124, 174

Dahshur 128, 135, 174, 181, 192, 207, 221, 229, 243, 252–254

deben (unit of measurement) 61

Deir el-Bahari 104, 122, 153, 155, 174

Deir el-Medina 79, 101, 139, 181, 232–233

Democritus 156–157

Dendera, temple of 31, 85, 149, 151, 153, 166, 170

deny (unit of measurement) 61

design 49, 73, 81, 90, 105, 117, 131, 142, 159, 162, 166, 176, 202, 204

diameter 66–67, 115, 127, 132, 156, 200–201, 215

Diodorus Siculus 70

division table, Byzantine 121

dja (unit of measurement) 61

Djedefra (Fourth Dynasty) xxi, 193, 225–226, 245

Djedkara-Isesi (Fifth Dynasty) xxi, 203, 226, 248

Djehuti-nefer Huia, house of 100

djeser (unit of measurement) 61

Djeserkaraseneb, tomb of 154

Djoser (Third Dynasty) xxi, 180, 181, 218, 226

Dra Abu el-Naga 104, 181, 232

‘doorkeeper’s rooms’ (elements of a tomb) 140

drawings (see also architectural and geometrical drawing) xiv, 18, 46, 47, 59, 81, 122, 157

   of buildings 96–101

   of a shrine on papyrus, from Gurob 2, 174

   scale drawings 54, 85, 101–112, 113, 174

Dynasty 0 xxi

Early Dynastic Period xxi, 124, 152, 162

Edfu, temple of 7, 85, 113, 149, 151, 162, 163, 166–173

Egina, temple at 13

Egyptian Mathematical Leather Roll 57

Eighth Dynasty xxi, 251

Eigtheenth Dynasty xxi, 100, 101, 104, 105, 109, 122, 124, 127, 140, 149, 154, 164, 181, 197, 232, 233

Elephantine 18–22, 47, 68, 105, 163, 166

Eleventh Dynasty xxi, 104, 149

ellipse 114, 115

   construction of 115–117

   drawing from the temple of Luxor 113

   elliptical vault in the tomb of Ramses VI 113, 114–115, 157, 158, 159, 218

Euclid 63, 65, 67, 68, 89, 240

extreme and mean ratio: see mean and extreme ratio

Ezbet Rushdi 206, 207, 211, 230, 254

&dfd; 24, 26, 28, 29, 30, 35, 54, 56, 57, 58–60, 67, 68, 78, 87, 175, 200

Fibonacci

   Leonardo from Pisa 26

   numbers 59, 67

   series 26, 35, 42, 56, 59, 67, 68, 79, 81

Fifth Dynasty xxi, 61, 182, 203, 206, 215, 226, 230, 231, 238, 246–249

Fifteenth Dynasty (Hyksos) xxi

finger (unit of measurement) 59–60, 61, 109, 111, 112, 115, 117–121, 132–133, 141, 146, 147, 167, 185, 212, 213–214, 219–221, 224–234, 242–254

First Dynasty xxi, 148, 156, 184

First Intermediate Period xxi, 150, 167, 228

formula xvi, 2, 4, 5, 58, 63, 81, 171

fortress at Semna South 149

foot (unit of measurement) 61

foundation ceremonies 42, 57, 131, 147, 148–153, 157–158, 171

   foundation deposits 149, 153, 155

   ‘stretching the cord’ 148, 149, 151–153, 155

four-pillared chamber of a tomb, drawing of 104, 105–109, 144, 147

Fourth Dynasty xxi, 113, 181, 192, 193, 197, 203, 206, 243–246

Fourteenth Dynasty xxi

fractions 58, 66, 67, 117–121, 167–173, 175, 212

   Horus-Eye 61, 68

   unit 58, 67

Freemasons 239

full-size sketches 113

Gebel Abu Foda 113, 117, 122, 167

Gebel Barkal 181, 234

geometry 2, 4, 178, 201, 202, 225, 234

   geometrical drawing of an ellipse from the temple of Luxor 113

   geometrical figures xiv, 5, 10, 11, 15, 35, 54, 66, 68, 69, 70, 73, 78, 80, 81, 83, 87, 156, 176, 215, 240

   geometrical models 70, 204, 213, 219, 221, 226–227, 234, 236–238, 240

   geometrical progression (see also numerical series) 58–59, 67

Giorgi, Francesco 3

Giza 2, 5, 181, 202, 206, 225, 226, 244, 245, 246

gnomonic expansion 26, 29

‘god’s passage’ (element of a tomb) 140

   ‘ . . . which is upon the sun’s path’ 140

Goethe, Johann Wolfgang 239

Golden Section 5, 10, 16, 22, 23, 28–31, 32, 35, 42, 46, 57, 60, 67–68, 78, 79, 80–85, 86, 173, 200

   names of 23

   psychological experiments 78–79, 80, 81, 85, 240

   tendency towards 69, 73, 78–80, 83, 85, 86, 240

   golden rectangle 83, 85

   golden triangle 201

Graeco-Roman Period 58

granite 206

Great Aten Temple 47, 99, 101, 155

‘Great Pyramid’ (see also pyramid of Khufu) 200–202

Greece 127, 138, 239

grids: see square grids

guide-lines 28, 81, 113–114, 122

Gurna 155

Gurob 174, 233

hall 49

   element of a tomb:

   ‘another hall of repelling rebels’ 140

   ‘chariot hall’ 140

   ‘hall of denial of access’ 140

   ‘hall of hindering’ 140, 141

   ‘hall of truth’ 140

   ‘hall in which one rests’ 140

handsbreath (unit of measurement) 61

harmony 2, 3, 4, 28

Harpedonaptai 157

Hawara 128, 138, 194

Hatshepsut (Eighteenth Dynasty) xxi, 122, 129, 153, 155, 183

hekat (unit of measurement) 61, 117

Heliopolis 100–101, 104, 182, 183

Hellenistic Period 127, 138, 175, 176, 240

Hemaka, tomb of 156

heptagon 42, 201

Heracleopolis xxi

Herodotus 70

heseb (unit of measurement) 61

Hetepsekhemwy (Second Dynasty) xxi, 180

hexagon 5, 11

Hierakonpolis 164–166

hinu (unit of measurement) 61

Horus-Eye fractions: see fractions

house 101, 128

   drawing of 104

   model of 128

   ‘house of gold’ 140

   of Djehuti-nefer Huia 100

   soul-houses 128

human body

   representation of 28–29, 81–83, 96, 97–99, 122

   proportions of 3, 5, 10, 28–29

Huni (Third Dynasty) 135, 181

Hyksos xxi

hypotenuse 22, 64, 67

Iby (Eighth Dynasty) xxi, 228, 251

icosahedron 68

Imhotep 10

Inenek-Inti, Queen of Pepi I (Sixth Dynasty) 249

Iput I, Queen of Teti (Sixth Dynasty) 219, 227, 228, 229, 230, 249

Iput II, Queen of Pepi II (Sixth Dynasty) 206, 228, 251

Iry, tomb of 232

Isis, Queen of time of Ramses VI (Twentieth Dynasty) 144

Islamic Period xxi

Itakajet, Queen no. 2 of Senusret I (Twelfth Dynasty) 251

el-Kab 105

Kalabsha, temple of 71–72, 101, 113, 123

Kamose (Seventeenth Dynasty) xxi, 232

Karnak 11, 31, 54, 105, 109, 123, 150, 155, 183

kha (unit of measurement) 61

Khaba (Third Dynasty) xxi, 181

khar (unit of measurement) 61

kha-ta (unit of measurement) 61

Khaemhat, tomb of 154

Khaemwaset, son of Ramses III (Twentieth Dynasty) 144

Khafra (Chefren, Fourth Dynasty) xxi, 203, 207, 219, 226–227, 236–238, 245

Khasekhemwy (Second Dynasty) 149

Khedival Period xxi

Khendjer (Thirteenth Dynasty) xxi, 183, 205, 206, 207, 208, 211, 212, 230, 254

Khentkawes, Queen of Menkaura (Fourth Dynasty) 181

Khentkawes, Queen of Neferirkara (Fifth Dynasty) 206, 207, 247

khet (rod, unit of measurement) 61, 117, 154

Khnum Hotep, tomb of 4

Khonsu, tomb of 232

Khui 228

Khuit, Queen of Teti (Sixth Dynasty) 227, 249

Khufu (Cheops, Fourth Dynasty) xxi, 13, 22, 28, 30, 31, 70, 200–201, 202, 203, 206, 207, 212, 213, 215–216, 219, 225, 226, 236–238, 244, 245, 246

Kircher, Athanasius 239

kite (unit of measurement) 61

Kom Ombo, temple of 172

Kuban 105

el-Kurru 181, 234

Lahun 206, 213, 252

land measuring 154

Late Dynastic Period xxi

Late Period xxi, 87, 104, 122, 128, 131, 159, 181, 182, 186, 213, 221, 224, 231, 234

Leonardo from Pisa, also called Fibonacci 26

limestone 128, 135, 138, 206

Lisht 104, 229, 230, 251

Lucas numbers 26

Luxor, temple at 28, 30, 113, 151

Macedonian Dynasty xxi

Macedonian Period xxi

Mammisi at Dendera 167

Martini, Francesco di Giorgio 28

mastaba 180, 181, 184, 192, 228, 249

   17 at Meidum 113, 114, 188–192

   of Ptahshepses 61

   Mastabat el-Faraƈun 113

mathematics 2, 4, 87, 89, 90, 117, 179, 200, 226

   Babylonian 64

   Egyptian 71, 87, 90, 202

   Greek 66, 67

   relationship with architecture xiv–xv, 179

   mathematical sources 57, 67, 68, 71, 90, 178, 203, 217, 218, 240

      Berlin Papyrus 217

      Egyptian Mathematical Leather Roll 57

      Kahun Papyri 57, 218

      Moscow Mathematical Papyrus 57, 154, 218

      Rhind Mathematical Papyrus (RMP) 57, 65, 154, 185, 218, 240

Mazghuna 254

mean and extreme ratio (see also Golden Section) 5, 22, 23, 67, 68

Medinet Habu 150

Meidum 113, 114, 184, 188, 192, 203, 212, 215–216, 221, 225, 226, 236–238, 244, 246

Meketra, models from the tomb of 128

Memphis 128, 133

Menkauhor (Fifth Dynasty) xxi, 248

Menkaura (Mycerinus, Fourth Dynasty) xxi, 113, 133, 181, 193, 206, 207, 226, 246

Menna, tomb of 154

Mentuhotep II Nebhepetra (Eleventh Dynasty) xxi, 104

Merenptah (Nineteenth Dynasty) xxi, 144

Merenra I (Sixth Dynasty) xxi, 203, 227, 250

Meritites, Queen of Pepi I (Sixth Dynasty) 250

Merneferra Ay (Thirteenth Dynasty) xxi, 183, 206, 211, 230, 254

Meroe 104, 181, 234

   monuments 56, 173, 234

   pyramids 178, 182, 192, 194, 197, 234

   temples 127

Middle Kingdom xxi, 47, 57, 58, 68, 70, 80, 104, 117, 122, 124, 138, 149, 156, 205, 208, 211, 217, 218, 221, 224, 228, 231, 234, 236, 238, 240

model (see also architectural and geometrical models) 226, 229, 240

module 23, 47, 71, 121–127

Mycerinus: see Menkaura

Nakht Min, tomb of 232

Napata xxi

Nebka (Fourth Dynasty?) xxi, 246

Nebnefer, tomb of 233

neby (unit of measurement) 61, 141

Nectanebo I (Thirtieth Dynasty) xxi, 85, 167

Nectanebo II (Thirtieth Dynasty) xxi, 172

Neferhetepes, Queen of Userkaf (Fifth Dynasty) 246

Neferirkara (Fifth Dynasty) xxi, 181, 203, 226, 247

Neferuptah, Queen or daughter of Amenemhat III (Twelfth Dynasty) 138, 254

Neith, Queen of Pepi II (Sixth Dynasty) 228, 250

Neuserra (Sixth Dynasty) xxi, 113, 149, 181, 184, 203, 206, 215, 247

New Kingdom xxi, 61, 88, 101, 104, 129, 131, 150, 153, 155, 158, 163, 172, 178, 180, 186, 213, 221, 224, 231, 234, 235, 240

Ninetjer (Second Dynasty) xxi, 180

Ninth Dynasty xxi

Nineteenth Dynasty xxi, 104, 112, 128, 144, 181, 197, 202, 233

Nofru, Queen no. 1 of Senusret I (Twelfth Dynasty) 219, 229, 230, 238, 251

Nubwenet, Queen of Pepi I (Sixth Dynasty) 249

number 2, 3, 60–63, 65, 68, 88, 166, 171, 187–188, 200

   integers (whole) 58, 60, 216, 218

   irrational 4, 24, 54, 68, 202

   numerical series (see also geometrical progression) 59, 167

numerologists 167, 201–202

Nubia 181, 233

Nuri 181, 234

obelisks 129, 131, 149, 156, 182–183, 184, 215

octagon 65, 66

Old Kingdom xvi, xxi, 2, 5, 64, 65, 71, 81, 87, 117, 122, 124, 149, 150, 156, 158, 159, 164, 178–179, 180, 192, 197, 204, 205, 207, 218, 221, 224, 226, 231, 234, 235, 236, 238, 240

orders

   Doric 175–176

   Ionic 175–176

Osireion 30

ostraca

   Cairo 25184 104, 142–146

   Cairo 25536 recto 140, 144

   Cairo 25537 140, 144

   Cairo 25538 140, 144

   Cairo 25581 recto 140, 144

   Cairo 50036 104

   Cairo 51936 104, 144, 147

   Cairo 66262 104

   Cairo 72452 140

   Cairo (number not known) 144

   Berlin B 144

   BM 8505 140, 144

   BM 41228 104

   BM 65944 (Nash 10) 144

   DeM (number not known) 144

   Gardiner 109 80

   mathematical from Elephantine 68

   Michaelides 53 144

   Michaelides 71 140

   Michaelides 92 144

   Strasburg H.112 139, 142, 144

   Turin 57036 140, 144

   Turin 57037 140, 144

Ottoman Period xxi

Palermo Stone 117, 149

Palladio 3

palm (unit of measurement) 59–60, 61, 88, 109, 112, 115, 117–121, 129, 132–133, 141, 146, 147, 167, 174, 185, 192, 203, 208, 212, 213–215, 219–234, 242–254

paradeigmata 138

Parthenon 13

papyri 101, 226

   Berlin 6619 217

   Budge 80

   Cairo 86637 verso 80, 144

   Demotic mathematical 58, 64, 217

   Kahun 57, 218

   Moscow Mathematical 57, 154, 218

   Ram. B 104

   Reisner 117, 218

   Rhind Mathematical 57, 65, 154, 185, 218, 240

   Sallier IV 80

   Turin 1885 recto 144, 147

   Turin 1885 verso 104, 144

   Turin 1923 142, 144

Penanhor, statue of 154

Pepi I (Sixth Dynasty) xxi, 159, 203, 227, 238, 249–250

Pepi II (Sixth Dynasty) xxi, 159, 183, 203, 206, 227, 228, 238, 250–251

perimeter 66, 90, 167, 200–203, 204, 228

peripteral

   chapels 105

   chapel(?) on a canal, drawing of 104, 109–112

   chapel from Deir el-Bahari, drawing of 104, 105, 107, 111

   temple at Elephantine 47

   temple of Tuthmosis III at Karnak 109–111

Persian Period, first and second xxi, 172

Petosiris, tomb of 28, 85

Philae 113, 117, 127

phoenix 182

&dfdf; 28, 60, 65, 67, 87, 175, 200, 202

Piranesi, Giovan Battista 239

plan (architectural) xiv, 10, 42, 43, 47, 54, 60, 71, 73, 83–84, 87, 90, 97, 100–101, 105–112, 122, 124, 127–128, 131–133, 138, 139, 141, 142–146, 147, 153, 155, 156, 158, 159, 167, 176, 186, 207, 216, 226, 240

Plato 2–3, 64, 88

   Platonic philosophy 3

   Platonic influence 64

Plimpton 322 64

Plutarch 64, 240

polygon 65, 66

Predynastic Period 43, 156, 162, 164

project 69, 70, 87, 90, 101, 109, 122, 135, 138, 140, 141, 142, 147, 166, 174, 175, 197, 206, 207, 221, 224

proportions xiv, 4, 11, 22, 70, 72, 112, 113, 117, 122, 129, 132, 159

   in architecture xiv, xv, xvi, 3, 6, 7, 16, 42, 47, 57, 69, 83, 85, 90, 101, 129, 131, 156, 171, 176, 194, 195, 203, 204, 205, 211, 212–213, 216, 219, 221, 226–227, 229, 232, 233, 236, 238, 239

   mathematical 5, 23, 24, 28, 29, 67, 68, 78, 79, 81, 85, 86, 219

   canon of 10

   of the human body 3, 5, 10, 28–29

Ptahshepses, mastaba of 61

Ptolemaic Dynasty xxi, 172

Ptolemaic Period xxi, 43, 113, 117, 138, 148, 150, 162–173, 236

Ptolemaic temples: see temples

Ptolemy xxi, 172

Ptolemy II xxi, 172

Ptolemy III xxi, 166, 171

Ptolemy VI Philometor xxi, 117, 167, 172

Ptolemy VIII Euergetes II xxi, 166, 172

Ptolemy X xxi, 167

Ptolemy XI xxi, 167

Ptolemy XII Auletes xxi, 166, 171

pylon 4, 101, 129, 131, 163

pyramidia (see also capstones) 138, 182–184, 186, 195, 205–211, 212, 231

   of Aamaket 232

   of Amenemhet III 183, 205, 206, 208, 211, 253

   from Dahshur 206, 207, 243

   from Ezbet Rushdi 206, 207, 230

   from Gurob 233

   of Iput II 206

   of Iry 232

   of Khendjer 183, 205, 206, 207, 208, 211, 230, 254

   of Khentkawes II, Queen of Neferirkara 206, 207, 247

   of Khonsu 232

   Late Period from Abydos 183, 197, 234

   of Merneferra Ay 183, 206, 211, 230, 254

   New Kingdom 183, 197, 233

   of Qaha 232

   of Queen GIIIa of Menkaura 206, 207, 246

   of a Queen of Neuserra (Lepsius 24 and 25) 206, 207, 230, 231, 248

   of the satellite of Khufu 206, 244

   of Sahura 183

   of Sekhemra-Wepmaat Intef V 232

   of Sennedjem 232

   of Senusret II 183, 206

   of the sun temples 184, 215

   of Tia and Tia 233

   truncated, from South Saqqara 206, 209–211, 230, 254

   of Turbay 232

   of Udjebten(?) 228, 250

   unfinished, from South Saqqara 206, 209–211, 230, 254

Pyramid Texts 4, 182, 184

pyramidologists 202

pyramids 4, 22, 64, 69, 70, 71, 83–138, 176, 180, 182, 184–185, 228, 231, 240

   ‘primeval’ 11–13, 15, 70

   queens’ 205, 236, 238

   satellite 133, 181, 197, 199, 203, 205, 206, 207, 212, 225, 227, 228, 229, 236, 238, 243, 244, 245, 246, 247, 248, 249, 250, 251

   step 133, 135, 180–181, 193, 216, 226, 234, 244, 247

      model of 128, 131–133, 135, 194

      shape of steps 133

      ‘Buried Pyramid’ 181

      of Djoser at Saqqara 115, 133, 180, 184, 216, 218

      of Khaba 181

      ‘Layer Pyramid’ 133, 181

      at Meidum 133, 135, 181, 184, 186, 192, 197–199, 216, 225

      no. 29 at Saqqara 135

      of Sekhemkhet 133

      satellite of Meidum 133

      at Sinki 133–135

      small, dating to the reign of Huni 135, 181

      unfinished at Zawiyet el-Aryan 135

   true 69, 135, 181, 184, 213, 221, 226, 242–254

   base of 70, 178, 185, 192, 200–201, 203, 204, 207–211, 216, 219, 224, 225, 242–254

   drawings of: see architectural drawings

   casing of 133–135, 192–193, 197, 198, 203, 205, 212, 215, 216, 221, 225, 245, 247, 251, 252–254

   corner of 70, 186, 200, 203, 204, 208

   diagonal of 70, 187–188, 192, 204, 207

   face of 70, 178, 186, 188, 207–211, 215

   height of 70, 178, 185, 200–201, 202, 203, 204, 216, 219, 224, 242–254

   models of: see architectural models

   slope of (see also seked) 23, 69, 70, 90, 135, 178, 185, 188–193, 196, 197–199, 202–204, 205–211, 212, 221, 226, 228, 236, 238, 242–254

   vertical section of 69, 70, 185, 192, 194, 195, 201, 207–208, 214, 215, 219, 221, 234

   of Ahmose

      at Dra Abu el-Naga 181, 232

      at Abydos 181, 232

   of Amenemhat I 203, 229, 230, 251

   of Amenemhat II 229, 252

   of Amenemhat III

      at Dahshur 115, 174, 205, 212, 230, 253–254

      at Hawara 135–138, 230, 254

   of Ameny Qemau 230, 254

   at Aniba 233

   of Atmu-neferu, Queen of Senusret II 212, 252

   Beg. 8 at Meroe 192, 234

   Bent Pyramid 69, 70, 181, 192, 193, 203, 206, 207, 212, 215, 221–225, 243, 251

   of Djedefra 193, 225–226, 245

   of Djedkara-Isesi 248

   at Gebel Barkal 181, 234

   GIa, of a Queen of Khufu 212, 244

   GIb, of a Queen of Khufu 212, 244

   GIc, of a Queen of Khufu 212, 244

   GIIIa, of a Queen of Menkaura 246

   GIIIb, of a Queen of Menkaura 133, 181, 246

   GIIIc, of a Queen of Menkaura 133, 181, 246

   of Iby 228, 251

   of Inenek-Inti, Queen of Pepi I 249

   of Iput I, Queen of Teti 227, 228, 229, 230, 249

   of Iput II, Queen of Pepi II 228, 251

   of Itakajet, Queen n. 2 of Senusret I 251

   of Kamose 232

   of Khafra 203, 207, 219, 226–227, 245

   of Khendjer 205, 212, 230, 254

   of Khentkawes II, Queen of Neferirkara 247

   of Khufu 13, 22, 28, 30, 31, 70, 200–201, 202, 203, 212, 213, 215–216, 225, 226, 244, 245, 246

   of Khuit, Queen of Teti 71–72, 249

   at el-Kurru 181, 234

   Late Period 213, 221, 231, 234

   Lepsius 24 and 25 (of the Queens of Neuserra?) 183, 206, 207, 228, 231, 248

   Lepsius 29 (of Menkauhor?) 248

   at Meidum 203, 212, 215–216, 221, 225, 226, 236–238, 244, 245, 246

   of Menkaura 113, 193, 226, 246

   of Merenra 203, 227, 250

   of Meritites, Queen of Pepi I 250

   of Merneferra Ay 211, 230, 254

   Meroitic 178, 182, 192, 194, 197, 234

   Middle Kingdom xvi, 70, 178–179, 180, 204, 205, 221, 226, 231, 234, 236, 240

   of Nebka 246

   of Neferhetepes, Queen of Userkaf 246

   of Neferirkara 181, 203, 226, 247

   of Neferuptah, Queen of Amenemhat III 138, 254

   of Neith, Queen of Pepi II 228, 250

   of Neuserra 113, 203, 247

   New Kingdom 178, 213, 221, 231, 234, 235

   of Nofru, Queen no. 1 of Senusret I 219, 229, 230, 238, 251

   of Nubwenet, Queen of Pepi I 249

   at Nuri 181, 234

   Old Kingdom xvi, 71, 178–179, 180, 204, 205, 221, 226, 231, 234, 235, 236

   of Pepi I 159, 203, 227, 238, 249–250

   of Pepi II 159, 203, 227, 238, 250–251

   of the Queen of Djedkara 226, 248

   of the Queen of Khendjer 254

   of a Queen of Pepi I 250

   of the Queens nos. 3, 4, 5, 6, 7, 8 and 9 of Senusret I 229, 238, 251–252

   of the Queens nos. 1, 2, 3, 4, 5, 6, 7, 8 and 9 of Senusret III 229–230, 238, 252–253

   of Raneferef (Lepsius 26) 247

   Red Pyramid 181, 192, 199, 203, 206, 207, 219, 224–225, 229, 243

   Roman 234–235

   of Sahura 203, 226, 230, 247

   of Sekhemra-Wepmaat Intef V 232

   of Senusret I 79, 229–230, 251–252

   of Senusret II 213, 252

   of Senusret III 207, 212, 229, 252–253

   of Shepseskara 247

   of Snefru: see Meidum, Bent Pyramid and Red Pyramid

   at Soleb 234

   of Teti 154, 159, 203, 227, 249

   of Udjebten, Queen of Pepi II 207, 228, 250

   of Unas 212, 249

   of unknown owner at North Mazghuna 254

   of unknown owner at South Mazghuna 254

   of unknown owner at South Saqqara 209, 230, 254

   of Userkaf 203, 226, 246

   14 and 15 at Soleb 104, 186

Pythagoras 2, 60, 89

   Theorem of 60, 63–64, 65, 67, 216–217, 218

   Pythagoreans 2, 28, 60

   Pythagorean philosophy 3

   Pythagorean Triplets 60–65, 117, 157, 216–221

      3-4-5: see 3-4-5 triangle

      5-12-13 221, 232, 233, 234

      7-24-25 221, 232, 233, 234

      8-15-17 221, 229, 230, 249, 251, 253

      20-21-29 219, 224–225, 230

Qaha, tomb of 232

Qasr el-Sagha 124, 159, 226

quarry

   at Gebel Abu Foda 113, 117, 122, 167

   at Sheikh Said 105

quartzite 128, 129

Queen of Djedefra (Fourth Dynasty) 245

Queen of Djedkara (Fifth Dynasty) 226, 248

Queen of Khendjer (Thirteenth Dynasty) 254

Queens of Khufu (Fourth Dynasty)

   buried in GIa 212, 244

   buried in GIb 212, 244

   buried in GIc 212, 244

Queens of Menkaura (Fourth Dynasty)

   buried in GIIIa 206, 246

   buried in GIIIb 133, 181, 246

   buried in GIIIc 133, 181, 246

Queens of Neuserra (Fifth Dynasty) 183, 206, 207, 228, 230, 231, 248

Queen of Pepi I (Sixth Dynasty) 250

Queens nos. 3, 4, 5, 6, 7, 8 and 9 of Senusret I (Twelfth Dynasty) 229, 238, 251–252

Queens nos. 1, 2, 3, 4, 5, 6, 7, 8 and 9 of Senusret III (Twelfth Dynasty) 229–230, 238, 252–253

radius 66, 115, 121, 200, 202

Ramesseum 101, 104

Ramses II (Nineteenth Dynasty) xxi, 129, 140, 144, 151, 181, 233

Ramses III (Twentieth Dynasty) xxi, 142, 144

Ramses IV (Twentieth Dynasty) xxi, 112, 144, 147

Ramses V (Twentieth Dynasty) xxi, 142, 144

Ramses VI (Twentieth Dynasty) xxi, 113, 114, 115, 142, 144, 157

Ramses IX (Twentieth Dynasty) xxi, 112, 140, 141, 142–146

Ramsesnakht, tomb of 104

Raneferef (Fifth Dynasty) xxi, 247

ratio

   1:2 124

   2:3 90

   3:5 90

   5:4 112, 200–201

   8:5 200, 234

rectangle 5, 35, 54, 69, 78, 79, 81, 85, 88, 240

Red Pyramid: see pyramids

remen (unit of measurement) 61, 88, 192

Renaissance 2–3

‘resting place of the gods’ (element of a tomb) 140

Rhind Mathematical Papyrus (RMP) 57, 65

river-measure (unit of measurement) 61

ro (unit of measurement) 61

Roman Period xxi, 113

Rome 129, 172, 234

rope (see also cord) 115, 117, 154, 155–156, 158

Rosacrucians 239

sa (unit of measurement) 61

‘sanctuaries in which the gods of the west/east repose’ (elements of a tomb) 140

sandstone 104

Sahura (Fifth Dynasty) xxi, 183, 203, 212, 226, 230, 236, 247

Saqqara 104, 115, 133, 180, 181, 184, 203, 206, 209, 218, 226, 233, 246, 248–251, 254

scale 83, 127, 129–131, 132, 135, 138, 141

   drawings 54, 85, 101–112, 113, 174

Schinkel, Friedrick 239

Second Dynasty xxi, 180

Second Intermediate Period xxi, 57

secret xv, xvi, 4, 241

   knowledge 87–88

seked (slope) 185–186, 192–196, 203–204, 208, 213, 236

Sekhemkhet (Third Dynasty) xxi, 181

Sekhemra-Wepmaat Intef V 232

Semna South, fortress at 149

Senenmut

   statue of 154–155

   tomb of 104, 105

Sennedjem, tomb of 232

Sennefer, tomb of 124

Senusret I (Twelfth Dynasty) xxi, 79, 104, 105, 149, 183, 203, 219, 229–230, 238, 251–252

Senusret II (Twelfth Dynasty) xxi, 183, 206, 213, 229, 252

Senusret III (Twelfth Dynasty) xxi, 207, 212, 229–230, 238, 252–253

Serlio 3

Seshat 42, 57, 148, 149, 153

setat (unit of measurement) 61, 88, 117, 154

Sethnakht (Twentieth Dynasty) xxi, 142

Seti I (Nineteenth Dynasty) xxi, 30, 129–131, 181

Seti II (Nineteenth Dynasty) xxi, 144, 147

Seventh Dynasty xxi, 181

Seventeenth Dynasty xxi, 231

Shabaka (Twenty-fifth Dynasty) 2, 4

shaft (element of a tomb, see also well) 140, 141

shenaty (unit of measurement) 61

Shepseskaf (Fourth Dynasty) xxi, 181

Shepseskara (Fifth Dynasty) xxi, 247

shrine 131

   box, sketch on ostracon 112–113

   drawing on papyrus from Gurob 2, 174

   drawing on an ostracon from Deir el-Bahari 104, 105, 107, 111

Siptah xxi, 144, 147

Sixth Dynasty xxi, 159, 203, 219, 226, 238, 249–250

Sixteenth Dynasty xxi

sketch: see architectural drawings

slate 100, 104

slope

   of corridors of tombs 141

   of corridors of pyramids 218

   of tombs 141, 142

Small Aten Temple 73, 99

Snefru (Fourth Dynasty) xxi, 69, 149, 181, 184, 192, 197, 199, 203, 206, 221, 225, 226, 228, 236, 243–244

Socrates 88

solar cult 182–184

Soleb 104, 181, 186–187, 234

Spira, Fortunio 3

spiral 26

square 35, 42, 47, 49, 65, 66, 69, 70, 78, 79, 81, 85, 88–89, 90, 158, 200, 215

square grids 5, 69, 71, 81–83, 122–127, 140, 174

square root 88, 89

statuary

   Greek 7

   Egyptian 7

stelae 2, 5, 182

step pyramids: see pyramids

Strabo 70

Sudan 127, 173

sun temples: see temples

survey xiv, 10, 109, 132, 139, 147, 176

symbolism 65, 180, 184, 239, 240

symmetry 5, 78

   axis of 42

ta (unit of measurement) 61

Tawosret xxi, 140

Tell el-Yahudiya 128, 129

temples 4, 90

   at Corinth 13

   of the Concord at Agrigentum 13

   at Dendera 31, 85, 149, 151, 153, 166, 170

   at Edfu 85, 113, 149, 151, 162, 163, 166–173

   at Egina 13

   Egyptian 16, 28

   funerary temples of Teti, Pepi I and Pepi II 159, 219

   Great Aten Temple 47, 99, 101, 155

   Greek 13, 15, 127, 175

   of Hatshepsut at Deir el-Bahari 122, 153

   at Heliopolis 100–101

   at Hierakonpolis 164, 166

   of Horus at Aniba 155

   at Kalabsha 71–72, 113, 123, 172

   at Karnak 11, 31, 54, 105, 109, 123, 150, 155, 183

   of Khons at Karnak 4, 11

   at Kom Ombo 172

   at Luxor 28, 30, 113, 151

   Mammisi at Dendera 167

   at Medinet Habu 150

   of Mentuhotep at Deir el-Bahari 174

   Meroitic 127

   of Nectanebo I at Ashmunein 85

   New Kingdom 101, 129

   Osireion 30

   Parthenon 13

   peripteral at Elephantine 18, 47

   peripteral of Tuthmosis III at Karnak 109–111

   at Philae 117, 127, 151, 167, 172

   primeval 161–162, 166

   Ptolemaic 7, 71–72, 85, 127, 129, 151, 159, 162–173, 176, 226–227

   at Qasr el-Sagha 124, 159, 226

   Ramesseum 101

   rock-cut 141

   of Satet at Elephantine 163–164, 166

   of Seti I at Heliopolis 149

   Small Aten Temple 73, 99

   sun temples 182, 184

      of Neuserra 149

      of Userkaf 215

   at Tôd 47, 129, 131–133, 135, 149

   valley temple of Amenemhat III at Dahshur 135

Tenth Dynasty xxi

Teti (Sixth Dynasty) xxi, 154, 159, 203, 219, 226–227, 229, 230, 249

theatre

   Greek 90

   Roman 90

Thebes xxi, 4, 104, 109

Themistius 66

Theorem of Pythagoras: see Pythagoras

Third Dynasty xxi, 104, 113, 115, 180, 181, 192, 193, 205, 216

Third Intermediate Period xxi, 172

Thirteenth Dynasty xxi, 205, 206, 207, 209, 211, 230–231, 254

Thirtieth Dynasty xxi, 85, 234

Ti, chapel of 5

Tia and Tia, tomb of 233

Titian 3

Tôd

   model of the temple of 128, 129, 131–133

   temple at 47, 129, 131–133, 135

tombs 90, 135, 155

   rock-cut 69, 83–175

   royal 83, 109, 139–147, 153, 174

   of Aamaket at Deir el-Medina 232

   of Amenhotepsesi 154

   of Amenmesse (KV 10) 142

   of Djeserkaraseneb 154

   of Hemaka 156

   of Iry at Deir el-Medina 232

   K94.1 at Dra Abu el-Naga 232–233

   of Khaemhat 154

   of Khaemwaset, son of Ramses III (QV 44) 144

   of Khnum Hotep at Beni Hasan 4

   of Khonsu at Deir el-Medina 232

   KV 55 141

   of Meketra 128

   of Menna 154

   of Nakht Min at Deir el-Medina 232

   of Nebnefer at Deir el-Medina 233

   New Kingdom 181

   Old Kingdom 122

   of Petosiris 28, 85

   of Qaha at Deir el-Medina 232

   of Queen Isis, time of Ramses VI (QV 51) 144

   of Ramses III (KV 11) 142

   of Ramses IV (KV 2) 112, 144, 147

   of Ramses V–VI (KV 9) 113, 114, 115, 142, 144, 157

   of Ramses IX (KV 6) 112, 141, 142–146

   of Ramsesnakht at Dra Abu el-Naga 104

   Royal Tomb of Amarna 83–84, 141

   of Senenmut, no. 71 at Thebes 104

   of Sennedjem at Deir el-Medina 232

   of Sennefer 124

   of Sethnakht (KV 11) 142

   of Seti I (KV 17) 181

   of Seti II (KV 15) 147

   of Siptah (KV 47) 147

   of the sons of Ramses II (KV 5) 181

   of the sons of Ramses III 144

   of Tia and Tia at Saqqara 233

   of Tawosret 140

   of Turbay at Deir el-Medina 232

   of Tutankhamun (KV 62) 181

   no. 1138 at Deir el-Medina 233

   no. 1225 at Deir el-Medina 233

   no. 1301 and 1302 at Deir el-Medina 233

‘treasuries’ (elements of a tomb) 140

triangles 5, 10, 11–15, 16, 18, 23, 35, 42, 47, 49, 54, 67, 69–72, 85, 88, 171, 207, 242–254

   with base equal to height (b=h) 208, 214–215, 226–227, 228, 230, 233, 248, 249–250, 251–252, 253

   ‘Egyptian’ 10, 11, 22, 23, 70

   equilateral 10, 11, 13, 22, 23, 69, 70–72, 90, 154, 208, 214–215, 221, 225, 228, 234, 243, 245, 253

   isosceles 10, 35, 42, 71, 245, 248, 250

   right-angled 4, 10, 28, 35, 60–63, 66, 71, 115, 117, 159, 185, 192, 193–194, 195–196, 203–204, 213, 214, 215, 216, 218, 219, 221, 236

   similar 158

   1:2 35, 42, 47, 54

   1:4 35, 42, 47, 54, 186

   1:8 35, 42, 54

   3-4-5 10–22, 23, 35, 47, 54, 60, 64–65, 70, 71, 115–117, 154, 157, 158–159, 217–218, 219, 245, 246, 247, 249, 250

   8:5 10, 11, 23, 35, 42, 43, 47, 54, 56, 70–71, 72, 78, 154, 225, 234

   14:11 215

Turbay, tomb of 232

Tutankhamun xxi, 181

Tuthmosis I (Eighteenth Dynasty) xxi, 183

Tuthmosis III (Eighteenth Dynasty) xxi, 4, 109, 129, 150, 155

Twelfth Dynasty xxi, 104, 128, 135, 203, 206, 231, 251–254

Twentieth Dynasty xxi, 104, 105, 112, 113, 114, 115, 144, 158, 159, 181, 218

Twenty-eight Dynasty xxi, 144

Twenty-fifth Dynasty xxi, 2, 81, 234

Twenty-first Dynasty xxi

Twenty-fourth Dynasty (Saite) xxi

Twenty-ninth Dynasty xxi, 54

Twenty-second Dynasty xxi

Twenty-seventh Dynasty xxi

Twenty-sixth Dynasty xxi, 181

Twenty-third Dynasty xxi

Udjebten, Queen of Pepi II (Sixth Dynasty) 183, 207, 228, 250

Unas (Fifth Dynasty) xxi, 212, 249

unit fractions: see fractions

units of measurement 59–60, 61, 66, 88, 124, 129, 132, 141, 154, 155, 201, 234

Userkaf (Fifth Dynasty) xxi, 203, 215, 226, 236, 246

Valley of the Kings 104, 105, 113, 114, 139, 140, 142, 153

Valley of the Queens 139, 140

vertical section of pyramids: see architectural drawings and pyramids

Vitruvius 28, 70, 88, 89, 90, 175–176

well (element of a tomb, see also shaft) 141

Window of Appearance 99

wooden boards, documents on 104, 109

Workmen’s Village at Deir el-Medina 129

Zawiyet el-Aryan 133, 135, 181, 246



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