Clavius, Christoph - Geometria practica

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135105LIBER TERTIVS.11
Vt A a, differentia Quotientum \\ qui fiunt, ſilat{us} quadrati \\ per vtramque vmbram rectam \\ diuidatur, # ad A a, differentiam \\ ſtationum notam in \\ menſura aliqua: # ita A F, \\ vt 1. # ad AF, \\ diſtan- \\ tiam,@

63[Figure 63]

hoc eſt, ſi differentia ſtationum diuidatur per dif-
ferentiam Quotientum, efficietur nota diſtantia
AF, in partibus differentiæ ſtationum A a, & c.

3. Si denique in ſtatione inferiori latus vm-
brærectæ ſecetur in E, & in ſuperiori ſtatione latus
vmbræ verſæ in H, reducenda quo que erit vmbra
recta ad verſam, vt diximus, & producendum la-
tus D C, vmbræ verſæ vſque ad punctum N, ſu-
mendaque D I, ipſi d H, æqualis. Nam vt Num. 1.
oſtendimus, ſi fiat,

22
Vt N I, differentia vm- \\ brarum verſarum # ad Aa, differentiam \\ ſtationum: # Ita A D, lat{us} \\ quadrati # ad A F, di- \\ ſtantiam,

cognita rurſus erit diſtantia A F, in partibus differentiæ ſtationum A a.

ALITER.

Sine reductione vmbræ rectæ ad verſam ita quoque agemus. Numerus
qui fit ex recta vmbra B E, in vmbram verſam d H, auferatur ex 1000000. qua-
drato lateris 1000. reſiduumque ſit, O. Item ex vmbra recta B E, in latus qua-
drati 1000. fiat P. Et quoniam, vt initio huius libro in conſtructione quadrati
Numer. 6. oſtendimus, latus quadrati medio loco proportionale eſt inter vm-
bras B E, D N: Erit rectangulum ſub B E, D N, quadrato lateris æquale. 3316. ſexti.441. ſecundum. ergo rectangulum ſub B E, D N, æquale ſitrectangulis ſub D E, D I, & ſub B E,
N I: ſi rectangulum ſub B E, D I, auferatur ex rectangulo ſub B E, DN, id eſt,
ex 1000000. quadrato lateris A D, reliquum fiet rectangulum ſub
B E, N I; ac proinde cum D I, ipſi d H, ſi æqualis, fiet rectangulum ſub B E, D I,
ex vmbra B E, in vmbram d H; atque idcirco reliquum rectangulum ſub B E,
N I, (quod videlicet relin quitur, ſi rectangulum ſub B E, D I, ex quadrato late-
ris detrahatur, vt dictum eſt,) numero O, æquale erit. Eſt autem ex conſtru-
ctione rectangulum quo que ſub B E, vmbrarecta, & latere A D, numero P, æ-
quale. Igitur cum numerus B E, multiplicans N I, A D, producat O, P, 5517. ſept. erit O, ad P, vt N I, ad AD. Sed vt Numero 1. huius problematis demonſtra-
uimus, vt NI, differentia vmbrarum verſarum ad A a, differentiam ſtationum, ita
eſt AD, latus quadrati ad AF, & permutando vt NI, ad AD, ita A a, ad AF. Igi-
tur erit quoque O, ad P, vt A a, ad A F. Quamobrem ſi fiat,

66
Vt O, numer{us}, quirelinquitur \\ ſinumer{us} genit{us} ex vmbra \\ recta in verſam ex quadrato \\ lateris de@rahatur, # ad numerum P, \\ qui ex vmbra re- \\ cta B E, in lat{us} AD, \\ producitur: # Ita A a, diffe- \\ @entiaſtatio- \\ tionum # Ad AF, \\ diſtan- \\ tiam

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Scan	Original
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70
101	71
102	72
103	73
104	74
105	75
106	76
107	77
108	78
109	79
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111	81
112	82
113	83
114	84
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116	86
117	87
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119	89
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Scan	Original
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70
101	71
102	72
103	73
104	74
105	75
106	76
107	77
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109	79
110	80
111	81
112	82
113	83
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119	89
120	90