Clavius, Christoph - Geometria practica

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139109LIBER TERTIVS. eſt, vt BE, ad AB, ita AF, ad GF; erit permutando, vt BE, ad AF, ita AB, ad 114. ſexti. FG. Eademque ratione erit vt b H, ad a F, ita a b, ad FG; ac proinde erit, vt tota
BE, ad totam AF, ita ablata b H, vel B I, ad ablatam a F, cum vtraque propor-
tio ſit, quæ AB, vel a b, ad FG.

66[Figure 66]

Igitur erit quo que reliqua IE, ad reliquam A a, vt tota BE, ad totam AF, hoc
eſt, vt AB, ad FG, cum duæ hę proportiones eædem inter ſe ſint, vt paulò ant@
demonſtrauimus. Quo circa ſi fiat,

22
Vt IE, differentia vmbra- \\ rum rectarum # Ad Aa, differentiam ſta- \\ tionum: # Ita A B, quadrati \\ lat{us} 1000. # ad F G,

proſiliet nota altitudo FG, & adiuncta menſoris ſtatura FL, tota altitudo G L,
quęſita nota efficietur.

ALITER.

DIVIDE quadrati lat{us} 1000. per vtramque vmbram rectam, & minorem Quo-
tientem duc in differ entiam ſtationum, numerumque productum partire per differen-
tiam Quotientum. Si namque hic vltim{us} Quotiens ducatur in Quotientem maiorem
ex priorib{us} duob{us} Quotientib{us}, produc{et}ur altitudo quæſi@a in partib{us} differentiæ
ſtationum. Quod ita perſpicuum fi{et}.

Sit vmbra recta minor b H. 50. verbi gratia, & maior B E, 125. at differentia
ſtationum Aa, ſit 16. paſſuum. Et quia eſt, vt b H, ad a b, ita a F, quatenus 1. 334. ſexti. F G; ſi a b, 1000. diuidatur per b H, 50. indicabit Quotiens 20. rectam a F, in
F G, contineri vicies.

Sic etiam, quia eſt, vt BE, ad A B, ita AF, quatenus 1, ad FG; ſi A B, 1000. 444. ſexti. diuidatur per BE, 125. monſtrabit Quotiens 8. rectam AF, in FG, contineri o-
cties. Quia itaque A a, 16. paſſuum vna cum a F, continetur in FG, octies, fit vt
Aa, 16. paſſuum octies ſumpta, vna cum a F, octies quoque ſumpta, faciat 128.
paſſus, & a F, octies ſumptam, nimirum numerum ipſi F G, æqualem. Eſt

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Scan	Original
131	101
132	102
133	103
134	104
135	105
136	106
137	107
138	108
139	109
140	110
141	111
142	112
143	113
144	114
145	115
146	116
147	117
148	118
149	119
150	120
151	121
152	122
153	123
154	124
155	125
156	126
157	127
158	128
159	129
160	130

Scan	Original
131	101
132	102
133	103
134	104
135	105
136	106
137	107
138	108
139	109
140	110
141	111
142	112
143	113
144	114
145	115
146	116
147	117
148	118
149	119
150	120
151	121
152	122
153	123
154	124
155	125
156	126
157	127
158	128
159	129
160	130

Scan	Original
131	101
132	102
133	103
134	104
135	105
136	106
137	107
138	108
139	109
140	110
141	111
142	112
143	113
144	114
145	115
146	116
147	117
148	118
149	119
150	120
151	121
152	122
153	123
154	124
155	125
156	126
157	127
158	128
159	129
160	130