176146GEOMETR. 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.
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.
Deinde quia angulus AKB, in propinquiore ſpeculi poſitione 1122. primi.
angulis ACK, CAK, æqualis eſt, ſi angulus ACK, remotioris poſitionis detra-
hatur ex angulo AKB, poſitionis propinquioris: remanebit angulus CAK, no-
tus. Si igitur 2210. triang.
rectil.33
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,
gignetur hypotenuſa CA, remotioris poſitionis ſpeculi, in partibus differentiæ
poſitionum ſpeculi KC. Et ſi rurſus 4410. triang.
rectil.55
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,
procreabitur quoquehypotenuſa KA, propinquioris poſitionis ſpeculi, in eiſ-
dem partibus differentiæ poſitionum ſpeculi KC.
hatur ex angulo AKB, poſitionis propinquioris: remanebit angulus CAK, no-
tus. Si igitur 2210. triang.
rectil.33
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,
gignetur hypotenuſa CA, remotioris poſitionis ſpeculi, in partibus differentiæ
poſitionum ſpeculi KC. Et ſi rurſus 4410. triang.
rectil.55
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,
procreabitur quoquehypotenuſa KA, propinquioris poſitionis ſpeculi, in eiſ-
dem partibus differentiæ poſitionum ſpeculi KC.
ALITER.
2.
Per ſolos ſinus idem aſſequemur hocmodo.
Inuenta hypotenuſa CA,
vt proximè diximus, per ſinus. 6610. triang.
rectil.77
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,
Prodibit enim in Quotiente altitudo AB, nota in partibus hypotenuſæ inuen-
tæ CA. Quod ſirurſus 8810. triang.
rectil.99
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,
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.
vt proximè diximus, per ſinus. 6610. triang.
rectil.77
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,
Prodibit enim in Quotiente altitudo AB, nota in partibus hypotenuſæ inuen-
tæ CA. Quod ſirurſus 8810. triang.
rectil.99
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,
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.