GEOMETR. PRACT.
reperietur CB, maior diſtantia ſpeculi C, ab altitudine. Ex qua ſi auferatur K C,
differentia poſitionum ſpeculi, nota remanebit KB, minor diſtantia ſpeculiK,
ab eadem altitudine. Quæ etiam inuenietur, ſi fiat, vt KC, differentia prædicto-
rum angulorum, qui complementa ſunt angulorum incidentiæ in ſpeculo, ad
KB, tangentem minorem: Ita KC, differentia poſitionum ſpeculi ad aliud, vt
perſpicuum eſt.
160.1.
Vt K C, differentia tangentium \\ quæ complemẽtis angulorum in- \\ cidentiæ debentur, # ad A B, ſi- \\ num to- \\ tum # Ita K C, differentia po- \\ ſitionum ſpeculi # ad A B,
#
Rvrsvs
ſi fiat, # #
Vt K C, differentia complemen- \\ torum angulorum incidenti
[?]
æ in \\ ſpeculo, # ad C B, tangento
[?]
m \\ maiorem: # Ita K C, differen- \\ tia poſitionum \\ ſpeculi # ad C B,
Deinde
quia angulus AKB, in propinquiore ſpeculi poſitione duobus
angulis ACK, CAK, æqualis eſt, ſi angulus ACK, remotioris poſitionis detra-
hatur ex angulo AKB, poſitionis propinquioris: remanebit angulus CAK, no-
tus. Si igitur fiat,
gignetur hypotenuſa CA, remotioris poſitionis ſpeculi, in partibus differentiæ
poſitionum ſpeculi KC. Et ſi rurſus fiat,
procreabitur quoquehypotenuſa KA, propinquioris poſitionis ſpeculi, in eiſ-
dem partibus differentiæ poſitionum ſpeculi KC.
160.1.
22. primi.
10. triang.
rectil.
Vt ſin{us} anguli C A K, \\ differentiæ angulorum \\ incidentiæ # ad K C, differen- \\ tiam poſitionum \\ ſpeculi: # Ita ſin{us} anguli AKC, com- \\ plementi anguli AKB, ad \\ duos rectos in propinquio- \\ re poſitione ſpeculi # ad C A,
10. triang.
rectil.
Vt ſin{us} anguli C A K, \\ differentiæ angulorum \\ incidentiæ # ad K C, differentiam \\ poſitionum ſpeculi: # Ita ſin{us} anguli re- \\ flexionis ACK, in \\ remotiori poſitione \\ ſpeculi # ad K A,
161.
ALITER.
2.
Per
ſolos ſinus idem aſſequemur hocmodo. Inuenta hypotenuſa CA,
vt proximè diximus, per ſinus. fiat,
Prodibit enim in Quotiente altitudo AB, nota in partibus hypotenuſæ inuen-
tæ CA. Quod ſirurſus fiat,
producetur CB, maior ſpeculi diſtantia ab altitudine. Ex qua ſi ſubtrahatur KC,
differentia poſitionum ſpeculi, cognita etiam relinquetur diſtantia minor KB. Quæetiam, ſi inueſtigetur hypotenuſa KB, vt ſupra traditum eſt, reperietur: ſi
fiat, vt ſinus totus angulirecti B, ad hypotenuſam inuentam KB, ita ſinus anguli
BAK, complementi anguli in propinquiore poſitione ſpeculi, ad aliud, vt ma-
nifeſtum eſt.
161.1.
10. triang.
rectil.
Vt ſin{us} tot{us} angu- \\ lirecti B, # ad hypotenuſam \\ inuentam C A, # Ita ſin{us} anguli A C B, \\ remotioris poſitionis \\ ſpeculi # ad A B,
10. triang.
rectil.
Vt ſin{us} tot{us} an- \\ gulirecti B, # ad hypotenuſam in- \\ uentam C A, # Ita ſin{us} anguli B A C, comple- \\ menti anguli in remotiore poſi- \\ tione ſpeculi # ad C B,
