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# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
# Folio 612, page id 867984570:0648
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.89
# 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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612
P APPVS AL, F X A N D F
0ns HIoc Cst
Nv. 
234
15C
10000
00
00
200
L NVS.
NIV. c. N0, ZPd.
13104
Eienres, quas Pappus innuie, sristaresbi demonttrationes, tujusmodi suite puo:
000.
In linea aliqua erecta, ut o a ponantur quottibet rectae continuae proportionales (seu in pro-
srectione Geomerrica) ab o inchoacae omnes, de terminatae ad L a aa aaa, ec. OUX reprxsentENE
numeros ab + continue proportionales: e quidem, (posito a =- 20,) numeros L, FO, 100, 100O, CEC.
quos AnalogoS rocemus.
Et, in recta huie normali, rectae continux quorlibet, quarum guxelibet ipA OT, EQuetE:
Adeoque O F, 02, 0 3, ec. continue crescentes aequalicer (teu in progreltione Prichmetica,) nu-
MerOS I, 2, 3, _c. repraesentantes.
Adeoque (PEOPtEF O L = L,) erit item quadraTUI E, E, = L X F = T; quod itaque reprasen-
tet unitatem.
Si itaque pariter repraesentandus (c numerus aliquis alius ciptra terminatus, puta 20, hoc est
2 X 20, seu 2a; propter Analosum an promoreatur alticudo, uno gradu, ab r id a: e Propter
Fundum 2, ampliecur balis (duplando) ab F ad 2. Cumque rectansula sine inter se in rarione
compotica ex basium et alcicudinum racionibus; erit 2. a rectangulum, quadraci F, F, bis decu-
plum; hoc eA risccuplum: adeoque cum F, 2, quadratum sit L; erit 2 a rectangulum, 20.
Si vero ducendus sic hic numerus 20, in alium quemris, pura 300, hoc elt 3 X 200, Ieu 3a4:
propcer Analosum 100 = aa promorenda erit altirudo, duobus acttruc gradibuo, ab a 7 aaa; e
propier fundum 3, eriplicanda balis 02, ut tiat 06: Adeoque, propier cencuplatam ascudinem
ec triplicatam balin rectangulum 6 aaa, exit rectanguli 2a, ter cencupla, hoc elt trecencupla;
cumque SC 2 a == 20, erit 6 aaa numerus factus ex 20 in 300.
EF Sic concinue quoccunque fuerinc numeri concinue mulciplicandi: nempe, balis continue mul.
cipticanda erie per lequentem fundum; et alticudo per sequentem analoguni, hoc est eoc gradibus
promorenda elt quot analogus ille postulat.
Ouod s Facienda est mulciplicario per numerum qui non in ciptra cerminetur: manente quae
prius erat alcicudine, toties eric mulciplicanda batis; (propter rectansula aeque alca, in batium.
suarum ratione:) Suvilicerque, si analosi fundus Ac F; manence quae prius bali, (quia mulcipli-
catio ver F nihil mutat,) promovenda erit alcimdo prour poltulat analosus.
Ouoclibet isitur numeris sic incer se continue mulciplicatis; quae randem provenie batis, nu-
merum reprae sentabit qui sic ex fundis inter se concinue mulciplicatis; quaeque provenie alcicudo,
qui sic sic ex analogis: Sed batis in alricudinem ducta, exhiber rectangulum quod factum repralen.
cat ex numeris exvolitis continue mulciplicaris, uc oltentum est. Urgo, Factus ex fundis in ta-
ctum ex analogis, exhribet factum ex numeris expoliris continue incer se mulciplicatis. Ouod
crat demonttrandum.