Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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vicies ſumpta eidem FG, æqualis. </
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<
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">Igitur 128. </
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<
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xml:space
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">paſſus, vna cum a F, octies ſumpta
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æquiualent ipſi a F, vicies ſumptæ. </
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<
s
xml:id
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xml:space
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">Si ergo vtrobique auferatur a F, octies ſum-
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pta, reliqui erunt 128. </
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<
s
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xml:space
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">paſſus æquales ipſi a F, duodecies ſumptæ. </
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>
<
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xml:space
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">Quare ſi 128.
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</
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<
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">diuiduntur per 12. </
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<
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">prodibunt 10 {2/3}. </
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<
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xml:space
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">paſſus pro recta, a F, cum hic Quotiens in
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12. </
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<
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<
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xml:space
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">Cumigitur a F, contineatur vicies in F G: </
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<
s
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xml:space
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">ſi a F, 10 {2/3}. </
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<
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xml:space
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<
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paſſuum ducatur in 20. </
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<
s
xml:id
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xml:space
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">pro creabitur altitudo F G, 213 {1/3}. </
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<
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">paſſuum. </
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<
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xml:space
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minorem Quotientem 8. </
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<
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xml:space
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">in differentiam ſtationum paſſuum 16. </
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<
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">ductam eſſe, vt
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gignerentur 128. </
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<
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xml:space
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">& </
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<
s
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xml:space
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">hunc numerum diuiſum eſſe per 12. </
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<
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xml:space
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">differentiam Quotien-
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tum, vt pro dirent paſſus 10 {2/3}. </
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<
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<
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">ac tandem hunc Quotientem 10 {2/3}. </
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<
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<
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ductum eſſe in 20. </
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<
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xml:space
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">Quotientem maiorem, vt produceretur altitudo F G, paſ-
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ſuum 213 {1/3}. </
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<
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xml:space
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cedentem viam, ſi nimirum fiat, vt 75. </
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<
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xml:space
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">differentia vmbrarum rectarum, ad diffe-
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rentiam ſtationum, nimirum ad 16. </
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<
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">paſſus. </
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<
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">ita quadrati latus 1000. </
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Nam 16. </
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<
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">ducta in 1000. </
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<
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xml:space
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">& </
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<
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">productus numerus 16000. </
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<
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">diuiſus per 75. </
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<
s
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xml:space
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">facit Quo-
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tientem 213 {1/3}. </
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<
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">veluti prius.</
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<
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">3. </
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<
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in remotiore ſtatione inter-
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<
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140-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/140-01
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ſecetur vmbra verſa in E, & </
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<
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">in propinquiore
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vmbra recta in H, vt in 3. </
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<
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ducta vmbra verſa adrectam, vt in Quadrati
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conſtructione Num. </
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<
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<
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pſimus: </
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<
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xml:space
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">ſi fiat, vt IN, differentia vmbrarum re-
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ctarum ad A a, differentiam ſtationum, ita A B,
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latus Quadrati 1000. </
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<
s
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xml:space
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">ad aliud, procreabitur al-
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titudo F G, quemadmodum Num. </
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<
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dimus.</
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<
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<
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fortè in vna ſtatione tranſiret linea fiduciæ, aut filum perpendiculi per
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punctum C, aſſumendum eſſet in primo caſu latus C D, vmbrę verſę in duo-
<
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bus autem aliis caſibus latus BC, vmbrę rectæ.</
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<
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head
>
<
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<
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">Sine reductione vmbrę verſę ad rectam ita agendum erit. </
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<
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">Numerus, qui fit
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ex vmbra verſa D E, in vmbram rectam b H, auferatur ex 1000000. </
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<
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xml:space
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">quadrato
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lateris 1000@ reſi duumque ſit P. </
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<
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xml:id
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xml:space
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">Item ex vmbra verſa DE, in latus 1000. </
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<
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</
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<
s
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xml:space
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"> Et quoniam ob triangulorum ſimilitudinem eſt, vt BN, ad BA, ita AF, ad F G:</
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<
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position
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xlink:label
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note-140-01a
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xml:space
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">4. ſexti.</
note
>
Etpermutando, vt BN, ad AF, ita BA, ad FG. </
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<
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">Sed vt BN, vmbra recta maior ad
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A F, diſtantiam, ita eſt I N, differentia vmbrarum rectarum ad A a, differentiam
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ſtationum, vt Num. </
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<
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<
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<
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<
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">dictum eſt. </
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<
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">Igitur erit quoque IN, ad Aa,
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ſicuti AB, ad FG: </
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<
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xml:id
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xml:space
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">Et permutando IN, ad AB, vt Aa, ad FG. </
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>
<
s
xml:id
="
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xml:space
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">Dico iam ita eſſe
<
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P, ad Q, vt IN, ad AB. </
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>
<
s
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"> Quoniam enim eſt, vt DE, ad AD, ita AB, vel AD,
<
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xml:space
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">4. ſexti.</
note
>
BN:</
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<
s
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xml:space
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"> erit rectangulum ſub DE, BN, ęquale quadrato numero 1000000. </
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<
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<
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symbol
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xlink:label
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xml:space
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">17. ſexti.</
note
>
AB, 1000. </
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<
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"> Eſt autemrectangulum ſub DE, BN, æquale rectangulis ſub DE,
<
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xml:space
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BI, & </
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<
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">ſub DE, IN. </
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<
s
xml:id
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xml:space
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">Igitur ſi productum ex vmbra verſa DE, in B I, hoc eſt, in
<
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vmbram rectamb H, dematur ex rectangulo ſub DE, BN, hoc eſt, ex quadrato
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1000000. </
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>
<
s
xml:id
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xml:space
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">remanebit rectangulum ſub DE, IN. </
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>
<
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xml:id
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xml:space
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">Ac propterea P, fiet ex DE, in
<
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IN. </
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>
<
s
xml:id
="
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xml:space
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">Fit autem Q, ex eadem vmbra verſa DE, in latus AB, 1000. </
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<
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xml:id
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">Igitur cum DE,
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multiplicans IN, & </
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<
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">AB; </
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>
<
s
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">producat P, Q, erit P, ad Q, ſicut IN, ad AB; </
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<
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xml:space
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">17. ſexti.@</
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>
eſt, ſicut Aa, ad FG. </
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<
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