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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 418, page id 845634801:0424
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 74 lines, status machine
# Lines: 74 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

18
V A RFORRM DE REDVS NTA ZREM A ZICYB
adsequendum rectangula.
pendiculari; ca caurione, it la calis cerminis Calvi supersine ac illibari, qui lutticianl au
Ad ret c d pcor spharicorum rpo quareiar.
Ripleurum Cphaericum contlicunne, cres maximi circuli in sphaera de(cripri
circuli, Sermenta circulorum, lunt peripherixe Jsona Bavouvai-
3 Anguli, quem bini quique maximi circuli, in murua corum sectione esticiune, aell
maneur in circumterentia maximi circuli. sub puncto sectionis eanquam polo deleripea
quanca ab illis duobus maximis circulis incercipitur.
Sectores circulorum, quorum sunr segmenta laceratripleuri Sphaerici, angulum lo.
lidum consticument Cenero sphaeia.
5 leaque duo larera quomodo. cunque lumpra, lune majora reliquo.
6 Fria durem lacera simul juncta, luneminoca circulo.
7
Ermajuslacus majori angulo opponitui.
8 Si peripheria cA lemicirculus, sectores angulum non consticuune in centro sphaetan
verum coincidum in eandem lineale Ca. Itaque quodliber lacus sphaerici eriangitu
minus elt semicirculo.
9 Producto auremuno lacere, angulus exterior minor est duobus angulisreliquis,
mul sumpris.
20 Sisub apicibus singulis propolui cripleuri sphaerici, describaneur maximi cireul
cripleurum ica descripcum, cripleuriprimum proxosici, laceribus ee angulis ett recipiu
cum.
12 Incriangulis sphaericis quorum eres anguli, aur eriam anguli duo proponuneurte
eti, factione res non indiger. Enimvero lacera cripleuri sphaerici, amplicudinibus eol
quibus opponuntur angulorum, eo casu lunexqualia. Fc conrea, angulorum amplicuc
nes sunclaceribus, quae ipsis opponuncur, aequales. Ec li dari duo angulituerine recli.
data quae iis opponuntur latera, non licobiccercium lacus angulum ve definire, pes cun
QuA PTODONUNEUT.
12 leaque circa earriangula, quorum angulus unus eAt rectus, dirigunur arcis prac
Pra. FE Aiquidem in iis rectangulis proponacur angulus aliguis obtulus aliquod. ve lal
majus quadranre, invercicur eiangulum nar ava onipus. Er cum idem criangulum qu
ruor modis variari poltic, ad quod cujulcunque sirmodi perrineane exdem sinvola
rectae, eligirur adsequenda ea species, quae ingulos, qui acurilune, extibec, de lale
quadcance minora. Ea enim ad lequuca, de specie propolica licet judicium facere d lu
ciocinari.
R EB perpendicularis demiccacur BC; Caetletur vero inplano AF. C ipsa C K per pCNC
cularis ad AE. Dico in primisan sulum K C B, esse angulo sphaerico B A C a qualettm
Duoniam enim planorum AF. C, A E. B, lectio communis est F A, cui ducuntur 
ophaes in plano quidem AEB secta B C; et in planu
AEC rectAK. C: ideo angulus acurus BC K ct
inclinatiO PLANORUM AF C, AE B. AE inclinaL
Tur eadem plana AF. C, AF B, circulive, per al
gulum sphaericum B A C. F. Kisirur angulus H CL
angulo sphaerico B A C aqualis. Ouod primolo
cotuir ostendendum.
Secundo dico angulos GKB, EKB esse L
a05.
Ouoniam enim recta linea AC, duabus rectis
CH, C. B sese muiuo secanribus in ( (ignO, ab
Circuli appellatione jam non exauditur plana figura. Semicirculus, Ouadran
13 Spharica rripleura rectansura rxvincs iea reducuntur ad plana.
Sir criangulum sphaericum ABC. cujus ansulus ad C rectus exittat, qui veco ad
aCUTUS. EL Ex E cencro sphaecae axancue semidiamerri E A, F. B, F C, et ad A P in plal
Elo
ducto
illeo
dure
circu
a
2t
lelt 1
eldem
est re
05
recta
sune,
recti
ciei
ex
20
SOr
Prot