Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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182FED. COMMANDINI nis, quouſque in unum punctum r conueniant; erit pyra-
midis a b c r, & pyramidis d e f r grauitatis centrum in li-
nea r h. ergo & reliquæ magnitudinis, uidelicet fruſti cen-
trum in eadem linea neceſſario comperietur. Iungantur
d b, d c, d h, d m: & per lineas d b, d c ducto altero plano
intelligatur fruſtum in duas pyramides diuiſum: in pyra-
midem quidem, cuius baſis eſt triangulum a b c, uertex d:
& in eam, cuius idem uertex, & baſis trapezium b c f e. erit
igitur pyramidis a b c d axis d h, & pyramidis b c f e d axis
d m: atque erunt tres axes g h, d h, d m in eodem plano
d a K l. ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
quæ lineam d h in u ſecet: per p uero ducatur x y æquidi-
ſtans eidem, ſecansque d m in

135[Figure 135] z: & iungatur z u, quæ ſecet
g h in φ. tranſibit ea per q: &
erunt φ q unum, atque idem
pun ctum; ut inferius appare-
bit. Quoniam igitur linea u o
æ quidiſtat ipſi d g, erit d u ad
112. ſexti. u h, ut g o ad o h. Sed g o tri-
pla eſt o h. quare & d u ipſius
u h eſt tripla: & ideo pyrami-
dis a b c d centrum grauitatis
erit punctum 11. Rurſus quo-
niam z y ipſi d l æquidiſtat, d z
a d z m eſt, utly ad y m: eſtque
ly ad y m, ut g p ad p n. ergo
d z ad z m eſt, ut g p ad p n.
Quòd cum g p ſit tripla p n;
erit etiam d z ipſius z m tri-
pla. atque ob eandem cauſ-
ſam punctum z eſt centrũ gra-
uitatis pyramidis b c f e d. iun
ctaigitur z u, in ea erit

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Scan	Original
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110
111
112
113	1
114
115	2
116
117	3
118
119	4
120

Scan	Original
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110
111
112
113	1
114
115	2
116
117	3
118
119	4
120