145115LIBER TERTIVS.
differentiæ ſtationum, nota relinquetur altitudo D F, vel d M, quæſita.
Inueniri
autem hac ratione rectam AF, demonſtratum eſt in problemate 4. Num. 1.
autem hac ratione rectam AF, demonſtratum eſt in problemate 4. Num. 1.
2.
Qvod ſi in vtraque ſtatione latus vmbræ verſæ ſecetur in F, H, vt in 2.
figura problematis 4. hic repetita, inuerſa tamen, habebimus tres vias inueſti-
gandi altitudinem A F, ex qua ſi tollatur latus quadrati A D, manifeſta relin-
quetur quęſita altitudo DF, vel d M. Nam reducta vtraque vmbra verſa ad re-
ctam, ſi fiat,
figura problematis 4. hic repetita, inuerſa tamen, habebimus tres vias inueſti-
gandi altitudinem A F, ex qua ſi tollatur latus quadrati A D, manifeſta relin-
quetur quęſita altitudo DF, vel d M. Nam reducta vtraque vmbra verſa ad re-
ctam, ſi fiat,
Vt I N, differentia vmbra- \\ rum rectarum, # ad A a, differentiam \\ ſtationum: # Ita A D, lat{us} qua- \\ drati 1000. # ad AF.
# Vel ſine reductione.
Vt P, numer{us}, qui fit ex \\ O H, differentia vmbra- \\ rum verſarum in a b, la- \\ t{us} quadrati, # ad numerum, qui fit ex vm- \\ bra verſa b H, maiore in \\ minorem B E, # Ita A a, diffe- \\ rentia ſtatio- \\ num # ad A F,
#### Vel
Vt A a, differentia Quotientum, qui \\ fiunt, ſi lat{us} quadrati per vtram \\ vmbram verſam diuidatur, # ad A a, differentiam ſta- \\ tionum notam in menſu- \\ ra aliqua # Ita A F, \\ vt 1. # ad A F,
procreabitur ſemper altitudo AF, ab oculo inſpectoris A, numerata:
quemad-
modumin problemate 4. Num. 2. demonſtratum eſt.
modumin problemate 4. Num. 2. demonſtratum eſt.
3.
Si denique in vna ſtatione ſecetur latus vmbræ verſę in E, &
in altera la-
tus vmbrę rectæ in H, vt in 3. figura problematis 4. hic inuerſo ordine repetita:
ſi vtin eodem problemate 4. Num. 3. demonſtrauimus, reducatur vmbra ver-
ſa ad rectam, & fiat,
tus vmbrę rectæ in H, vt in 3. figura problematis 4. hic inuerſo ordine repetita:
ſi vtin eodem problemate 4. Num. 3. demonſtrauimus, reducatur vmbra ver-
ſa ad rectam, & fiat,