# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 419, page id 845634801:0425
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=425
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000425.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

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RE SPONSORVM. LTBER VIII.
ctos angulos insistir: ideo plano GK B per ip la5
lineam ACF Tan Plac L C. Quare planum
GKE B, CHIE ad planuM A F. C rectum. Ad planum
aurem A L C, recum ele quoque planum BF C:
circulienim AC, CB lele muruo normalitet le.
ctos angulos ipla BK inliltic, ex 1deo ad omnes
rectas lineas quae iplam concingune X in lubjecto
sunc plano A E C quales G K, L B, rectos anguloS CMMLH. Suncigitur anguli C HB, F KB
recti. Onod Secundoloco fuir ostenden duin.
24 Cum eriangulum sphaericum proponitur obtiquangulum auc incerra adhuc spe-
ciei sed ex daris adsequendae, in duo rectangula quelaamodum ee planum resolvirur.
Aue criamBMet Ooquangulum sphaericum ad plan eu. Verum mechodus
Relolvitur eriangulum obligtangulum in duo rectanoula, demista ab aliquo angulo-
rum ad latus quod ei opponitur peripheria orthogonia. LTague CteMS maximuS, cujuS
Deripheria MMIa ctlegmencum, educendus est per poloscirculi, a quo ablumitur latus an-
Curandum aurem est ea eductiore, ur ex datis rerminis salvi supertinc ac illibari, qui
25 Siucerque angulorum ad balin changuli spharicituern ee aectioIs, pe.
ripheria at angulo verticis ad baliu demilta, cadic inera criangulum; led si diverla,
CXTEA.
17 Sicctarsuli Sphaet ctes anguli tuerincacuri, latera quoque minOTA CrUNE qua-
1o Siceriangulum sphaericum AB D, de in peripheriam BD cadac segmentum ortho-
Primum dico esse cransTinuolant aS Da C. ad cransinuolam anguli D A C, siCuE
Prolinum pecipliella a Dad prolinum peripheria AD.
ducto, ad anoulos rectoserit. Per iplam aurem
CAHE ex HYBOMLICI, Qura ansas  CB propOni
tur rectuS. Ec horum planotu BD, BLC
cidem plano A F. C rectorum, communis lectio
estrecta K B. Ilaque eidem plano AF. C ad re.
illa videcur hac expedicioi.
Sulo parodico opposicum.
Cuthiane ad adsequendum rectarsa.
16 Si ceuracrianguli sphaerici fuerine majora quadeanre circuli; bals vero quadcans
aur quadrante major: anguli omnes erune obculi.
alanre circuli.
sonii AC.
guli D.
Sccundo dico esse transtinuolam peripheria C B ad cranstinuolam peripherix CD,
licur cranssinuolam peripherix AB ad cransinuolam peripherix A L
Lercio dico elle linum C  al uu B licuc peolinum ansl  da Peontum alt
Denique de quarro dico esse linum alsu A C ad linum angult  A C, LCuE EAuL
lnuolam ansuli Dad crantunuolam ansuli B.
V. Zrian.