10171LIBER SECVNDVS.
Vt H E, differentia Tangentium \\ angulorum obſeruationum # Ad FD, ſi- \\ num totum # Ita H E, vel F G, differen- \\ tia ſtationum # ad F D,
VFG, differentia \\ Tangentium cõ- \\ plemẽtorum an- \\ gulorum obſer- \\ uationum, # Ad CE, \\ ſinum to- \\ tum # Ita F G, diffe- \\ rentia ſtatio- \\ num interfe- \\ neſtr{as}, # ad C E, \\ longitudi- \\ nem pro- \\ poſitam,
35[Figure 35]44
Vt F G, differentia \\ Tangentium com- \\ plementorũ angu- \\ lorũ obſeruationũ # ad G C, Tangen- \\ tem complemen- \\ ti minoris angu- \\ li obſeruati # Ita F G, ad GC, \\ differentia ſta- \\ tionum inter \\ feneſtr{as}
gignetur longitudo optata C E, in partibus differentiæ ſtationum H E, vel F G,
& c. Quod ſi rurſus fiat,
11 & c. Quod ſi rurſus fiat,
Vt H E, differentia Tangentium \\ angulorum obſeruationum # Ad FD, ſi- \\ num totum # Ita H E, vel F G, differen- \\ tia ſtationum # ad F D,
2.
Sediam ex duabus feneſtris F, G, inſpiciatur extremum E, per angulos
CFE, CGE, ducaturq; FH, ipſi GE, parallela. Quoniã igitur angulus C F 2229. primi. angulo CGE, æqualis eſt: ſi ponatur ſinus totus C E, erit C G, Tangens anguli
CEG, complementi minoris anguli obſeruationis G, & CF, Tangens anguli
CEF, complementi maioris anguli obſeruationis C F E: at F G, differentia ſta-
tionum, hoc eſt, interuallum inter feneſtras, differentia erit dictarum Tangen-
tium. # Quamobrem ſi fiat,
33 CFE, CGE, ducaturq; FH, ipſi GE, parallela. Quoniã igitur angulus C F 2229. primi. angulo CGE, æqualis eſt: ſi ponatur ſinus totus C E, erit C G, Tangens anguli
CEG, complementi minoris anguli obſeruationis G, & CF, Tangens anguli
CEF, complementi maioris anguli obſeruationis C F E: at F G, differentia ſta-
tionum, hoc eſt, interuallum inter feneſtras, differentia erit dictarum Tangen-
tium. # Quamobrem ſi fiat,
VFG, differentia \\ Tangentium cõ- \\ plemẽtorum an- \\ gulorum obſer- \\ uationum, # Ad CE, \\ ſinum to- \\ tum # Ita F G, diffe- \\ rentia ſtatio- \\ num interfe- \\ neſtr{as}, # ad C E, \\ longitudi- \\ nem pro- \\ poſitam,
Vt F G, differentia \\ Tangentium com- \\ plementorũ angu- \\ lorũ obſeruationũ # ad G C, Tangen- \\ tem complemen- \\ ti minoris angu- \\ li obſeruati # Ita F G, ad GC, \\ differentia ſta- \\ tionum inter \\ feneſtr{as}
PROBLEMA XII.
1.
Sit longitudo A B, &
menſor in extremo A, conſtitutus videre non poſ-
fit alterum extremum, niſi ad dextram ſiniſtramue
36[Figure 36]
recedat vſq;
adD, punctũ, è quo vtrumq;
extremũ
cerni poſsit. Eritigitur longitudo AB, menſori in
D, exiſtenti poſita in tranſuerſum. Quare ea per
problema 10. inueſtigabitur.
fit alterum extremum, niſi ad dextram ſiniſtramue
cerni poſsit. Eritigitur longitudo AB, menſori in
D, exiſtenti poſita in tranſuerſum. Quare ea per
problema 10. inueſtigabitur.