| version 1.19, 2002/08/18 16:32:39 |
version 1.20, 2002/08/18 16:37:02 |
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| <s>Quoniam enim <lb/>ponitur vt EB ad B <lb/>D, hoc e&longs;t vt rectan­<lb/>gulum EBD ad qua­<lb/>dratum BD, ita qua­<lb/>dratum DK ad reli­<lb/>quum quadrati AD, <lb/>erit componendo, & <lb/>conueniendo, vt <expan abbr="rectã">rectam</expan> <lb/>gulum BDE ad re­<lb/>ctangulum EBD, ita <lb/>quadratum AD ad <lb/>quadratum DK: &longs;ed <lb/>vt rectangulum BGE <lb/>ad <expan abbr="rectãgulum">rectangulum</expan> BDE, <lb/><figure id="fig159"></figure><lb/>ita e&longs;t quadratum MG ad quadratum AD; ex æquali <lb/>igitur, vt rectangulum BGE ad rectangulum EBD, ita <lb/>e&longs;t quadratum MG ad quadratum DK: &longs;ed vt rectan­<lb/>gulum EBD ad rectangulum EBG, ita e&longs;t quadratum <lb/>DK ad GO quadratum; ex æquali igitur vt rectangu­<lb/>lu m BGE ad rectangulum EBG, ita erit quadratum <lb/>MG ad quadratum GO: &longs;ed rectangulum BGE maius <lb/>e&longs;t totum parte rectangulo EBG; quadratum igitur MG <lb/>quadrato GO maius erit, & recta MG maior quàm <pb pagenum="82"/>GO: &longs;ecat igitur parabola KBL rectam MG in puncto <lb/>O. </s> | <s>Quoniam enim <lb/>ponitur vt EB ad B <lb/>D, hoc e&longs;t vt rectan­<lb/>gulum EBD ad qua­<lb/>dratum BD, ita qua­<lb/>dratum DK ad reli­<lb/>quum quadrati AD, <lb/>erit componendo, & <lb/>conueniendo, vt <expan abbr="rectã">rectam</expan> <lb/>gulum BDE ad re­<lb/>ctangulum EBD, ita <lb/>quadratum AD ad <lb/>quadratum DK: &longs;ed <lb/>vt rectangulum BGE <lb/>ad <expan abbr="rectãgulum">rectangulum</expan> BDE, <lb/><figure id="fig159"></figure><lb/>ita e&longs;t quadratum MG ad quadratum AD; ex æquali <lb/>igitur, vt rectangulum BGE ad rectangulum EBD, ita <lb/>e&longs;t quadratum MG ad quadratum DK: &longs;ed vt rectan­<lb/>gulum EBD ad rectangulum EBG, ita e&longs;t quadratum <lb/>DK ad GO quadratum; ex æquali igitur vt rectangu­<lb/>lu m BGE ad rectangulum EBG, ita erit quadratum <lb/>MG ad quadratum GO: &longs;ed rectangulum BGE maius <lb/>e&longs;t totum parte rectangulo EBG; quadratum igitur MG <lb/>quadrato GO maius erit, & recta MG maior quàm <pb pagenum="82"/>GO: &longs;ecat igitur parabola KBL rectam MG in puncto <lb/>O. </s> |
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| <s>Similiter o&longs;tenderemus candem parabolam &longs;ecare <lb/>quamcumque aliam in hyperbole ABC ordinatim ad dia <lb/>metrum applicatarum. </s> | <s>Similiter o&longs;tenderemus eandem parabolam &longs;ecare <lb/>quamcumque aliam in hyperbole ABC ordinatim ad dia <lb/>metrum applicatarum. </s> |
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| <s>Quoniam igitur &longs;unt octo magni <lb/>tudines quaternæ totæ, & ablatæ proportionales; ac pri­<lb/>mi quidem ordinis, vt rectangulum BDE ad rectangu­<lb/>lum BGE, ita quadratum AD ad quadratum MG: &longs;e­<lb/>cundi autem ordinis, vt rectangulum EBD ad rectangu­<lb/>lum EBG ita quadra <lb/>tum DK ad quadra­<lb/>tum OGD: &longs;ed vt <lb/>EB ad BD, hoc e&longs;t <lb/>vt ablata primæ in pri <lb/>mis rectangulum EB <lb/>D ad reliquum BD <lb/>quadratum, ita poni­<lb/>tur ablata primæ in &longs;e <lb/>cundis, quadratum D <lb/>K ad reliquum exce&longs; <lb/>&longs;um, quo quadratum <lb/>AD &longs;uperat quadra­<lb/>tum DK; vt igitur e&longs;t <lb/>reliqua primæ ad reli­<lb/>quam &longs;ecundæ in pri­<lb/><figure id="fig160"></figure><lb/>mis, ita erit in &longs;ecundis; videlicet vt quadratum BD ad <lb/>quadratum BG, ita reliquum quadrati AD dempto qua­<lb/>drato DK, ad reliquum qua rati MG dempto quadra­<lb/>to GO. </s> | <s>Quoniam igitur &longs;unt octo magni <lb/>tudines quaternæ totæ, & ablatæ proportionales; ac pri­<lb/>mi quidem ordinis, vt rectangulum BDE ad rectangu­<lb/>lum BGE, ita quadratum AD ad quadratum MG: &longs;e­<lb/>cundi autem ordinis, vt rectangulum EBD ad rectangu­<lb/>lum EBG ita quadra <lb/>tum DK ad quadra­<lb/>tum OGD: &longs;ed vt <lb/>EB ad BD, hoc e&longs;t <lb/>vt ablata primæ in pri <lb/>mis rectangulum EB <lb/>D ad reliquum BD <lb/>quadratum, ita poni­<lb/>tur ablata primæ in &longs;e <lb/>cundis, quadratum D <lb/>K ad reliquum exce&longs; <lb/>&longs;um, quo quadratum <lb/>AD &longs;uperat quadra­<lb/>tum DK; vt igitur e&longs;t <lb/>reliqua primæ ad reli­<lb/>quam &longs;ecundæ in pri­<lb/><figure id="fig160"></figure><lb/>mis, ita erit in &longs;ecundis; videlicet vt quadratum BD ad <lb/>quadratum BG, ita reliquum quadrati AD dempto qua­<lb/>drato DK, ad reliquum qua rati MG dempto quadra­<lb/>to GO. </s> |
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