Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Table of contents

[121.] LEMMA. I.

[122.] LEMMA. I I.

[123.] THEOREMA 9. PROPOS. 9.

[124.] SCHOLIVM.

[125.] I.

[126.] II.

[127.] III.

[128.] THEOREMA 10. PROPOS. 10.

[129.] COROLLARIVM.

[130.] THEOR. 11. PROPOS. 11.

[131.] LEMMA.

[132.] SCHOLIVM.

[133.] COROLLARIVM.

[134.] THEOREMA 12. PROPOS 12.

[135.] SCHOLIVM.

[136.] THEOR. 13. PROPOS. 13.

[137.] SCHOLIVM.

[138.] THEOREMA 14. PROPOS. 14.

[139.] FINIS LIBRI III. THEODOSII. AD LECTOREM.

[140.] CHRISTOPHORI CLAVII BAMBERGENSIS E SOCIETATE IESV SINVS, VEL SEMISSES RECTARVM IN CIRCVLO SVBTENSARVM: LINEAE TANGENTES: ATQVE SECANTES.

[141.] CHRISTOPHORI CLAV II BAMBERGENSIS E SOCIETATE IESV SINVS, VEL SEMISSES RECTARVM in circulo ſubtenſarum: LINEÆ TANGENTES, ATQVE SECANTES. PRÆFATIO.

[142.] DEFINITIONES. I.

Page: 112 (100)

[143.] II.

Page: 113 (101)

[144.] III.

Page: 113 (101)

[145.] Vel aliter.

Page: 113 (101)

[146.] IIII.

Page: 113 (101)

[147.] V.

Page: 113 (101)

[148.] VI.

Page: 113 (101)

[149.] VII.

Page: 113 (101)

[150.] LEMMA.

Page: 118 (106)

121109

THEOR. 1. PROPOS. 1.

IN Quadrante circuli ſumptis arcubus æqua-
11Perpĕdicu-
lares ex ar-
cubus qua-
drãtis ęqua
libus ad al-
terutrá ſe-
midiame -
trorum, vel
ad rectam
ſemidiame
tro paral -
lelam du-
ctę auferũt
fegm enta
inæqualia,
maiufq́ eſt
illud, qd al
teri femi-
diametro
{pro}pinquius
eſt. libus, ſi ab eorum terminis ad alterutram ſemidia-
metrorum, vel ad rectam ſemidiametro paralle-
lam, perpendiculares ducantur; erunt ſegmenta
ſemidiametri, velillius parallelæ interillas perpen-
diculares intercepta, inæqualia, maiusq́ erit illud,
quod alteri ſemidiametro propinquius elt.

SIT Quadrans ABC, in quo arcus æquales ſint DE, EF, à quorum ter-
minis ad ſemidiametrum AC, vel ad rectam RS, ipſi AC, parallelam per-
pendiculares ducantur DKG, ELH, FMI. Dico ſegmenta GH, HI, vel
KL, LM, inæqualia eſſe, maiusq́ue eſſe GH,

118[Figure 118] quàm HI, vel KL, maius, quàm LM. Com-
pleto enim ſemicirculo BCN, producantur
rectæ DG, EH, FI, vſque ad O, P, Q. Du-
ctis quoque rectis ET, FV, ad DO, EP, per-
pendicularibus, iungantur rectæ EO, FP.
Et quoniam arcus DE, EF, æquales ſunt,
2227. tertij. erunt anguli quoque DOE, EPF, illis inſi-
ſtentes, æquales: Sunt autem & recti anguli
T, V, æquales. Igitur cum tres anguli trian-
guli EOT, tribus angulis trianguli FPV,
ſint æquales; quòd tam illi, quàm hiduobus
3332. primi. rectis ſint æquales; erit & reliquus angulus
TEO, reliquo angulo VFP, æqualis: ac
propterea æquiangula erũt triãgula EOT,
444. @exti. FPV. Quare erit vt OE, ad ET, ita PF, ad
5515.tertij. EV: Eſt auté recta OE, maior, quàm recta
PF; quod illa centro propinquior ſit, quàm
hęc. Igitur & recta ET, maior eſt, quàm re-
cta FV. Cum ergo recta ET, æqualis ſit
6634. primi. ſegmentis GH, KL, ob parallelogramma
TH, TL; & recta FV, ſegmentis HI, LM,
ob parallelogramma VI, VM; erit quoque ſegmentum GH, maius ſegmen-
to HI, & ſegmentum KL, ſegmento LM. In quadrante ergo circuli ſumptis
arcubus æqualibus, & c. Quod erat den. onſtrandum.

BREVIVS. Ducatur recta DF, ſecans ſemidiametrum ductam AE, in
Z, & rectam EH, in a, producaturq́ue recta FV, vſque ad b. Quoniam igi-
tur arcus DF, ſectus eſt biſariam in E, ſecta quoque erit recta DF, biſariam
in Z, ex lemmate in definitionibus poſito, ac proinde Da, maior erit

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