The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 14
... equal to DG , and DA , DB , parts of them , are equal therefore the remainder AL is equal to the remain- der ( 3. Ax . ) BG ; but it has been shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things ...
... equal to DG , and DA , DB , parts of them , are equal therefore the remainder AL is equal to the remain- der ( 3. Ax . ) BG ; but it has been shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things ...
Side 15
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R angle ABC to the ...
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R angle ABC to the ...
Side 16
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Α Because AF is equal to AG , and AB to AC , the two sides ...
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Α Because AF is equal to AG , and AB to AC , the two sides ...
Side 17
... equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
... equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
Side 18
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ...
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore