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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 373, page id 845634801:0379
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intet
prina
1
aED. G
n
MOTUC
testas.
Ietest
id
RESPONSORDM. LEBER VTTI.
cubo = B quad. in D cub. 10. F B quadr. - quadr. in D 5. Perpendiculum B in D quad.-
quad. 5. - B cubo in D quad. 10 F B quad. - cubo.
Proponatur criangulum rectansulum cujus basis 10. perpendiculum r. es aneulus acurus eju sdem
telligatur smpiao.
Ad trianculum anculi criplis slatuerur basis 970. perpendiculum 299
Aa trianeulum anculi quadrupit, stacuerur basis 9 401. perpendiculum 3960
Ad erianculum anculi quintupli, Stacueeur basis 90050. perpendiculum 490Ot.
Et cum angulus acucus primi crianguli deprehendetur esse.
PART. SCRVD.SEC.
erit angulus acurus secundi 2I 25
teriii 17
quarit 22 50
26
2
quinei 28 33 10.
Cum aurem factorum nequse fieri subtractio, argumemum est angulum mulciplum esse obeusum.
eogue casus nihilominus excessus factorum adsignabitur lateri, es angulus subtensus intelligitur exte.
tior mulcipl
A L F F F R.
SiFuerine erianoula rectangula quoccunque, et horum secundi anoulus
acucuS SE duplus ad acutum primi, tertii eriplus, quarci quadruplus, quin-
ei guincuxlus, e eo continuo nacurali progressu, primi aurem crianguli
Perpendiculum stacuatur prima proporcionalium, balis ejuldem secunda,
Caque Series COnFInUCtUE.
In secundo, exit balis ad perpendiculum, ut cerria, minus prima, ad sc-
cundam bis.
In certio, aEguarta minus secunda ter, ad tertiam tex, minus prima.
In quartO, uE quinca, minus tertia sexies, plus prima, ad quartam quater,
minus secuncd Gllater.
Inquinto, uc sexta, minus quarra decies, plus secunda quinquies, ad
quintam quinquies, minus certia decies, plus pria.
In sexto ut teptima, minus quinta quindecies, plus cerria quindecies,
minusprima, ad sextam sexies, minus quarta vicies, plus secunda sexies.
In seprimo, ut octara Minus sexta ricies semel, plus quarta tricies quin-
quies, minus secunda septies, ad seprimam sepries, minus quinta cricies
Quinquies, plus certia ricies semet, minus prima.
ELIEAM MAICLI, Mriburis luccessire in duas partes proportionali
bus secundum earum seriem, utrobigue primum adtrmaris deinde nesa-
tis, _ lumptis mulciplicibus, ut ordo graduum in arriticiosa Seneli pOte.
Carum, quibus ex addicuntur, exisit.
F H E OR E M a II
St L TerMInO diAMCEI SUMANEUE in CirCUIO CIFCIHHICLCMEX GUOECUI.
que aequales, ee ab altera extremicare educantur linex rectae adlumpta
rum circumferentiarum aequalium cerminos: cductae hunc bales criangu
lorum rectangulorum, quorum communis hyporenula est diameter; ac
balis quidem diameero proximior incelligitur balis ansuli simpli, succedens
dupli, e eo continuo ordine. Constitmatur aurem leries lincarum recta-
Cum continue proportionalium; quarum prima, lit ae qualis Lemidiameero;
ecunda bali anguli simpli.
ad trianculum anguli dupli, stacuecur basis 99. perpendiculum 20.