464444GEOMETRIÆ
319[Figure 319]
Sit ſpiralis ex prima reuolutione orta, AOVE, primus circulus,
EYG, ſumptum in ſpirali vtcumq; punctum, V, & centro, A, in-
teruallo autem, AV, circulus deſcriptus, VHX. Dico portionẽ,
AOVA, comprehenſam ſpiralis portione, AOV, & recta, AV, eſ-
ſe {1/3}. portionis eiuſdem circuli comprehenſæ rectis, AV, AC, &
circumferentia, VHXC. Exponatur triangulus rectangulus, HkF,
rectum habens angulum, FKH, cuius latus, HK, æquale ſit ipſi,
AC, & kF, circumferentiæ, CXHV, erit ergo triangulus, HFk,
æqualis portioni circuli, cuius baſis eſt circumferentia, CXHV;
112. huius.
10. l. 4. deſcripta deinde intelligatur parabola, F℟H, cuius vertex, H,
quam tangat, KH, in, H, & , FK, ſit axi eiuſdem æquidiſtans.
Dico trilineum, H℟Fk, eſſe æqualem ſpatio circumferentia, VHX
C, ſpirali, VOA, & recta, AC, contento (quod ſpatium breuitatis
cauſa dicatur reſiduum portionis circuli, VHC,) ſi enim non, erit
co maius, vel minus, ſit primò maius, & vt in antecedenti trilineo,
H℟Fk, figura circumſcripta intelligatur ex triangulo, HM3, &
ex trapexijs, P3, ℟4, F6, compoſita, & alia inſcripta ex
EYG, ſumptum in ſpirali vtcumq; punctum, V, & centro, A, in-
teruallo autem, AV, circulus deſcriptus, VHX. Dico portionẽ,
AOVA, comprehenſam ſpiralis portione, AOV, & recta, AV, eſ-
ſe {1/3}. portionis eiuſdem circuli comprehenſæ rectis, AV, AC, &
circumferentia, VHXC. Exponatur triangulus rectangulus, HkF,
rectum habens angulum, FKH, cuius latus, HK, æquale ſit ipſi,
AC, & kF, circumferentiæ, CXHV, erit ergo triangulus, HFk,
æqualis portioni circuli, cuius baſis eſt circumferentia, CXHV;
112. huius.
10. l. 4. deſcripta deinde intelligatur parabola, F℟H, cuius vertex, H,
quam tangat, KH, in, H, & , FK, ſit axi eiuſdem æquidiſtans.
Dico trilineum, H℟Fk, eſſe æqualem ſpatio circumferentia, VHX
C, ſpirali, VOA, & recta, AC, contento (quod ſpatium breuitatis
cauſa dicatur reſiduum portionis circuli, VHC,) ſi enim non, erit
co maius, vel minus, ſit primò maius, & vt in antecedenti trilineo,
H℟Fk, figura circumſcripta intelligatur ex triangulo, HM3, &
ex trapexijs, P3, ℟4, F6, compoſita, & alia inſcripta ex