Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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tria autem Min. </
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<
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<
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ratione, ſi quis deſideret quotlibet gradus, ac Minuta, inquirenda
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prius erit particula Minutorum, quæ deſiderantur, eaque ad gradus propoſitos
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adijcienda. </
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<
s
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xml:space
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">Quod ſi particula minutorum inuentorum tam exigua fuerit, vt
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circino vix accipi poſsit, accipienda ea erit vnà cum 1. </
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<
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<
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">& </
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<
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</
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<
s
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xml:space
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<
s
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xml:space
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">particula conflatus adijciendus ad numerum graduum propoſitum
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minus vno. </
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<
s
xml:id
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xml:space
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">Vt ſi velit quis grad. </
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<
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<
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<
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<
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nuta. </
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<
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<
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xml:space
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">particulæ arcus X Y, in Quadrantem B C, transferantur. </
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Nam particula in 60. </
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<
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">gradu complectetur 59. </
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<
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">Min. </
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<
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<
s
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xml:space
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">Siigitur arcus
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ex illa particula, & </
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<
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<
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<
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<
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">grad. </
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<
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arcus grad. </
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<
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<
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<
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<
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xml:space
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">Eademque ratio eſt de cæteris. </
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<
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xml:space
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">Accipientur autem in ar-
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cu XY, particulæ 59. </
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>
<
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xml:space
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">ſi vnus pes circini in puncto 50. </
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>
<
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xml:space
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">ſtatuatur, & </
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>
<
s
xml:id
="
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xml:space
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">alter in nona
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particula primæ partis ſextæ totius arcus XY, verſus X. </
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>
<
s
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="
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xml:space
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">Ita accipientur quoque
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particulæ 49. </
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<
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<
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<
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<
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">&</
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<
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">c. </
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<
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">vt perſpicuum eſt.</
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<
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<
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vero ſi Minutanonin Quadrante BC, ſed in maiori, minoriue accipien-
<
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da ſint, inquirenda ea erunt in Quadrante B C, beneficio arcus X Y, vt docui-
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mus; </
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<
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xml:space
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">Deinde arcuiinter C, & </
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<
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">finem particulæ inuentæ auferendus ex Quadrã-
<
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te propoſito arcus ſimilis. </
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>
<
s
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">quod fiet, ſi ille Quadrans ex centro A, deſcribatur,
<
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rectaque ex A, per finem particulæ in B C, inuentæ educatur, &</
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<
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<
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<
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Num. </
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<
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<
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xml:space
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">præcedenti diximus, perbelle etiam quadrant in lineas
<
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<
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xlink:label
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xml:space
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">Quo pactore-
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peri
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atur fra-
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ctio cuiuſque
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particulæ in
<
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parte qualibet
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lineæ rectæ in
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part{es} æqual{es}
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diuiſæ.</
note
>
rectas. </
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<
s
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xml:space
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">Nam eadem ratione cognoſcemus, ſi linea recta in quotuis partes æqua-
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les ſecetur, quantam fractionem quælibet particula vnius partis contineat: </
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<
s
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xml:space
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">Et
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viciſsim quo pacto ex vna parte abſcindenda ſit quæcun que fractio propoſita.
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</
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<
s
xml:id
="
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xml:space
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">Quæ res incredibile eſt, quantam vtilitatem cum alijs rebus Geometricis, tum
<
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ver ò maxime Dimenſionibus, quæ per ſcalam altimetram fieri ſolent, afferat, vt
<
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lib. </
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<
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<
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xml:id
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xml:space
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">cum de Quadrato Geometrico, vbiſcalæ altimetræ vſus apparebit, perſpi-
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cuum erit. </
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<
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xml:id
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xml:space
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">Sit enim recta linea A B, vt ad pedem Quadrantis ſuperioris vides,
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ſecta in 10. </
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<
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xml:space
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<
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xml:space
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">(In totenim partes libet tam vmbiam rectam, quam
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<
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37
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verſam ſcalæ altimetræ diſtribuere: </
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<
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<
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</
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<
s
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xml:space
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">quod per illam diuiſionem facilius Dimenſiones perficiantur, vt ſuo loco pate-
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bit. </
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<
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xml:space
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">Magis tamen probarem, ſi vtrumque vmbræ latus in 100. </
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<
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xml:space
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">partes ſecare-
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tur, ſi id magnitudo inſtrumenti commode permittit) propoſitumque ſit, quot
<
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partes decimas contineat particula D C, partis quintæ. </
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>
<
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xml:space
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">Beneficio circini ſum-
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pta paiticula D C, decupletur ab A, vſque ad E. </
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<
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xml:space
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">Et quoniamin A E, continen-
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tur ſex partes totius lineæ A B, continebit propterea particula D C. </
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<
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">{6/10}. </
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<
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partis decimæ, hoceſt, {6/100}. </
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<
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">totius lineæ. </
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<
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xml:space
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">Ita vt ſirecta A B, diuiſa cogitetur in
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100. </
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<
s
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xml:space
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">partes, tribuendo ſingulis decimis partibus denas particulas, ſegmentum
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A C, comprehendat {46/100}. </
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<
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xml:id
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xml:space
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">Quia vero vltra {6/10}. </
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<
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xml:id
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xml:space
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">ſupereſt adhuc particula F E,
<
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vnius decimæ, ſi ea rurſum decupletur ab A, vſque ad G, reperientur in A G,
<
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/>
octo partes totius lineæ A B. </
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>
<
s
xml:id
="
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xml:space
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">Continet ergo particula F E, {8/10}. </
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<
s
xml:id
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xml:space
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">vnius decimæ,
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hoc eſt, propoſita particula D C, vltra {6/10}. </
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<
s
xml:id
="
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xml:space
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">vnius partis rectæ A B, continet in
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ſuper {8/10}, vnius decimæ, (vnius inquam decimæ ex illis {6/10}. </
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<
s
xml:id
="
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xml:space
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">quas in particula
<
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D C, diximus comprehendi) nimirum {8/100}. </
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<
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">vnius partis. </
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<
s
xml:id
="
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xml:space
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">ſi ſingulæ partes deci-
<
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mærectæ A B, diuiſæ eſſent in 100. </
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<
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xml:id
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">particulas; </
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>
<
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xml:id
="
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xml:space
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">atque adeo, ſi recta A B, ſecta
<
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intelligatur in 1000. </
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>
<
s
xml:id
="
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xml:space
="
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">partes, tribuendo ſingulis decimis partibus centenas par-
<
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ticulas ſegmentum A C, complectetur {468/1000}. </
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>
<
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