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" BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate... "
The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Σελίδα 21
των Royal Military Academy, Woolwich - 1853
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...(I. 4) and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which the equal sides are opposite. Therefore the angle BAE is equal to the angle EC F. But the angle ACD is greater than the angle ECF therefore the angle...

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...the other angles to the other angles, each to each, to which the equal sides are opposite ; [I. 4. therefore the angle ACB is equal to the angle CBD....angles ACB, CBD equal to one another, AC is parallel to BD. [I. 27. And it was shewn to be equal to it. Wherefore, the straight lines &c. QED PROPOSITION...

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...remaining angles of the one are equal to the remaining angles of the other, each to each ; viz., those to which the equal sides are opposite. Therefore the angle ACB is equal to the angle CB ] >. Because the straight line BC meets the two straight lines AC, BD, and mftlcff the alternate...

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...As ABC, BCD, AB = CD, BC is common, L ABC = L BCD, .-. Base AC = base BD, and L ACB = L CBD (I. 4). And because the straight line BC meets the two straight lines AC, BD, and makes the alternate Z,s ACB, CBD equal, AC is || to BD (I. 27), And it was shown 'to be equal to it. Wherefore the straight...

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...other angles, each to each, to which the equal sides are opposite ; [I. 4. therefore the angle ACS is equal to the angle CBD. And because the straight...straight lines AC, BD, and makes the alternate angles ACS, CBD equal to one another, AC is parallel to BD. [I. 27. And it was shewn to be equal to it. Wherefore,...

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...the equal sides AB, CD are opposite ; therefore the angle ACB is equal to CBD. (I. 4) •And because BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal ; therefore AC is parallel to BD. (I. 27) And AC was shown to be equal to BD. Therefore, the straight...

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...the base GC is equal to DF, and the triangle GBC to DEF, and the other angles to the other angles, each to each, to which the equal sides are opposite ; therefore the angle GCB is equal to DFE; but DFE is, by the hypothesis, equal to BCA ; wherefore also the angle BCG is...

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...is equal to the base , and the triangle to the triangle , and the other angles to the other angles, each to each, to which the equal sides are opposite; therefore the angle is equal to the angle ; but the an^le is equal to the angle ; therefore the angle is equal to the angle...

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...to the triangle c ef, and the remaining angles of one triangle to the remaining angles of the other, each to each, to which the equal sides are opposite ; therefore the angle bae is equal to the angle e cf. But the angle ecd is greater than the angle e cfTherefore the angle...

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...to the triangle c ef, and tue remaining angles of one triangle to the remaining angles of the other, each to each, to which the equal sides are opposite ; therefore the angle 6 ae is equal to the angle ec f. But the angle ecd is greater than the angle ec /. Therefore the angle...




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