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 Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Side 17
... demonstrated . 1 THE PROP . V. THEOR . HE angles at the bafe of an Ifofceles triangle are equal to one another ; and , if the equal fides be produced , the angles upon the other fide of the bafe fhall be equal . Let ABC be an Ifofceles ...
... demonstrated . 1 THE PROP . V. THEOR . HE angles at the bafe of an Ifofceles triangle are equal to one another ; and , if the equal fides be produced , the angles upon the other fide of the bafe fhall be equal . Let ABC be an Ifofceles ...
Side 22
... demonstrated , that two ftraight lines cannot have a common fegment . If it be poffible , let the two ftraight lines ABC , ABD have the fegment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
... demonstrated , that two ftraight lines cannot have a common fegment . If it be poffible , let the two ftraight lines ABC , ABD have the fegment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
Side 26
... demonstrated that the angle BCG , that is 4 , the angle ACD , is greater thari the angle ABC . Therefore , if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angles of a triangle are together less than two right angles . A A ...
... demonstrated that the angle BCG , that is 4 , the angle ACD , is greater thari the angle ABC . Therefore , if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angles of a triangle are together less than two right angles . A A ...
Side 27
... demonstrated , that BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. THE PRO P. XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a ...
... demonstrated , that BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. THE PRO P. XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a ...
Side 43
... demonstrated that no other line but AD is parallel to B BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E D. PROP . XL . THEOR . E QUAL triangles upon equal bases , in the fame ftraight line , and towards ...
... demonstrated that no other line but AD is parallel to B BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E D. PROP . XL . THEOR . E QUAL triangles upon equal bases , in the fame ftraight line , and towards ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore