The Elements of EuclidJohnson and Warner, 1811 - 518 sider |
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Side 21
... likewise their sides terminated in the other extremity ; but this is impossible ; therefore , if the base BC coincides with a 7. 1 . the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the ...
... likewise their sides terminated in the other extremity ; but this is impossible ; therefore , if the base BC coincides with a 7. 1 . the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the ...
Side 25
... likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b S. Ax ABD , the less to the ...
... likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b S. Ax ABD , the less to the ...
Side 27
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has ...
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has ...
Side 28
... likewise equal ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the B c D C angle ADC ; and because the angle BCD of the triangle DCB is greater than its angle BDC , and that the greater ...
... likewise equal ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the B c D C angle ADC ; and because the angle BCD of the triangle DCB is greater than its angle BDC , and that the greater ...
Side 31
... equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the base CB is greater than the base EF ; the angle BAC is likewise greater than the an- gle EDF . Book 1 . a 4. 1 . 24.1 . For OF EUCLID . 31.
... equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the base CB is greater than the base EF ; the angle BAC is likewise greater than the an- gle EDF . Book 1 . a 4. 1 . 24.1 . For OF EUCLID . 31.
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1806 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore