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 O F Euclid's Data in Like Manner CorrectedF. Wingrave, 1809 - 531 σελίδες |
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Σελίδα 9
... angle BAC 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 angle B ABC ...
... angle BAC 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 angle B ABC ...
Σελίδα 12
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is ... BAC is equal to the angle EDF . For , if the tri- angle ABC be ap- plied to DEF , so B D G that the point B be on E ...
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is ... BAC is equal to the angle EDF . For , if the tri- angle ABC be ap- plied to DEF , so B D G that the point B be on E ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal to ` 8 Ax . it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is to divide it into two equal angles . t Let BAC be the ...
... angle BAC coincides with the angle EDF , and is equal to ` 8 Ax . it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is to divide it into two equal angles . t Let BAC be the ...
Σελίδα 18
... BAC . 19 Bisecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
... BAC . 19 Bisecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
Σελίδα 19
... angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII .
... angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII .
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABC circumference common logarithm cone cylinder demonstrated described diameter 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 logarithm multiple opposite parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid 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 tiple triangle ABC triplicate ratio vertex