Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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<
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paro diuiſorem ex figura 2. </
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<
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20. </
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<
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xml:space
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<
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</
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<
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xml:space
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<
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xml:space
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<
s
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xml:space
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<
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xml:space
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go primum Quotientem 2. </
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<
s
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xml:space
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">ad ſiniſtram, numerum peculiarem
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<
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xlink:label
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note-310-01
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note-310-01a
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2--20--6.
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36.
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20. </
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<
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<
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<
s
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xml:space
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">ad dextrã, ſub quo ſcri-
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bo eius quadratum 36. </
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<
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<
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<
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hęc multiplico tres numeros 2. </
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<
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xml:space
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<
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<
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<
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<
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quadratum 36. </
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<
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">& </
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<
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<
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<
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">detraho, nihil que relinquitur,
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atque ita abſolutum eſt ſequens punctum: </
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<
s
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xml:space
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<
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iam diuiſorem ex toto Quotiente inuento 26, ducto in 20. </
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<
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xml:space
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">id eſt, in
<
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numerum peculiarem quadratæ radicis, quem inuenio 520. </
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>
<
s
xml:id
="
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xml:space
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">Et quia perhunc
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diuidi non poteſt punctum 52. </
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<
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">pono in Quotienteo. </
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>
<
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xml:id
="
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xml:space
="
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">neque opus eſt multipli-
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care, vtreperiatur numerus ſubtrahendus, quia nihil ſubrahitur, cumo. </
s
>
<
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xml:id
="
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xml:space
="
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">multi-
<
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plicans producato. </
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>
<
s
xml:id
="
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xml:space
="
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">Et ſic fit in omnibus alijs extractionibus, quando diuiſor
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inuentus in puncto propoſito ne ſemel quidem continetur: </
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<
s
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xml:space
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tum eſt punctum 52. </
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<
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">punctum queinſequens eſt 5201.</
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<
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<
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style
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iterũ diuiſorẽ ex toto Quotiẽte inuẽto 260. </
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<
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xml:space
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liarem 20. </
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<
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<
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<
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<
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go totum Quotientem prius inuentum 260. </
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<
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<
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<
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260--20--1
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1
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</
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>
numerum peculiarem 20. </
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<
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xml:space
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">in medio, & </
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<
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">quotientẽ 1. </
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<
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tumad dexteram, eiuſque quadratum 1. </
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<
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<
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<
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>
trium ſuperiorum numerorum facit 5200. </
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<
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dratum 1. </
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<
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">figuræ inuentæ 1. </
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<
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<
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">qui ex puncto 5201. </
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<
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<
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relinquit. </
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<
s
xml:id
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xml:space
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">Eſt ergo abſoluta extractio, radixque inuenta eſt 2601. </
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<
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xml:space
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">quæ quadra-
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tè, id eſt, in ſe multiplicata producit propoſitum numerum 6765201.</
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</
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<
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<
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<
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hæc eſt probatio, vel examen cuiuſuis extra ctionis, vt videlicet ra-
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dix inuenta in ſemultip licetur vel quadratè, vel cubice, vel ſurdeſolide, &</
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<
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<
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qualitateradicis. </
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<
s
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xml:space
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">Si enim in extractione nihil fuit relictum, veluti in noſtro exẽ-
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plo, neceſſe eſt, numerum productum ęqualem eſſe propoſitio numero, ex quo
<
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/>
fa cta eſt extractio: </
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<
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xml:space
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">Si autem in extractione aliquid fuit relictum, illud additũ
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producto numero conficiet numerum propoſitum. </
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<
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<
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men per 9. </
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<
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<
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">vt in Diuiſione. </
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<
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xml:space
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<
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">vel 7.
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</
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<
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<
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">reſiduum collocetur tum in ſiniſtra parte crucis, tum in
<
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dextra, quod Quotiens, vel radix inuenta ſit etiam inſtar Diuiſoris. </
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<
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xml:space
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reſiduo in ſe multiplicato quadrate, vel cubice, &</
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<
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<
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<
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<
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<
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vel 7. </
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<
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xml:id
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xml:space
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">neceſſe eſt, reſiduum hoc æquale eſſe reſiduo numeri propoſiti, ſi abijciã-
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tur ex eo omnia 9. </
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<
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">vel 7. </
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<
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">& </
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<
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">nihil in extra ctione relictum ſit. </
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<
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<
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fig-310-01
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fig-310-01a
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number
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208
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310-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/310-01
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quin ex reſiduo extractionis, & </
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tiplicatæ abijcienda erunt omnia 9. </
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<
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">vel 7. </
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<
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xml:id
="
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xml:space
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">Hoc enim reſiduum ęquale
<
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eſſe debetreſi duo numeri propoſiti, ſi omnia 9. </
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<
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<
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">abijciantur. </
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<
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">In
<
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noſtro exemplo, ſi probatio inſtituatur per 9. </
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<
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xml:space
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">reſiduum ſemper eſto.
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</
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<
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="
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xml:space
="
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">Siverò fiat per 7. </
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>
<
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="
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"
xml:space
="
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">ſtabit exemplum examinis vt hic apparet.</
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</
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<
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<
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<
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>
ex numero 239483190. </
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<
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">extrahenda radix cubica.</
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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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