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 CorrectedDesilver, 1829 - 516 sider |
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Side 26
... join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the angle B ADC ; and because the angle BCD of A D the ...
... join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is greater than the angle B ADC ; and because the angle BCD of A D the ...
Side 31
... join AH ; and because BH is equal to EF , and AB to DE , the two AB , BH are equal to the two DE , EF each to each ; and they contain equal angles ; therefore the base AH is equal to the base DF , and the trian- gle ABH to the triangle ...
... join AH ; and because BH is equal to EF , and AB to DE , the two AB , BH are equal to the two DE , EF each to each ; and they contain equal angles ; therefore the base AH is equal to the base DF , and the trian- gle ABH to the triangle ...
Side 34
... join AD ; and at the point A , in the straight line AD , make ( 23. 1. ) the B D C angle DAE equal to the angle ADC ; and produce the straight line EA to F. Because the straight line AD , which meets the two 34 BOOK I. THE ELEMENTS OF ...
... join AD ; and at the point A , in the straight line AD , make ( 23. 1. ) the B D C angle DAE equal to the angle ADC ; and produce the straight line EA to F. Because the straight line AD , which meets the two 34 BOOK I. THE ELEMENTS OF ...
Side 36
... join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal ... Join BC ; and because AB is parallel to CD ; and BC meets them , the alter- nate angles ABC , BCD are equal ( 29. 1 ...
... join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal ... Join BC ; and because AB is parallel to CD ; and BC meets them , the alter- nate angles ABC , BCD are equal ( 29. 1 ...
Side 39
... Join BE , CH ; and because BC is equal to FG , and FG to ( 34. 1. ) EH , BC is equal to EH ; and they are parallels , and joined towards the same parts by the straight lines BE , CH ; but straight lines which join equal and parallel ...
... Join BE , CH ; and because BC is equal to FG , and FG to ( 34. 1. ) EH , BC is equal to EH ; and they are parallels , and joined towards the same parts by the straight lines BE , CH ; but straight lines which join equal and parallel ...
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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 |
Vanlige uttrykk og setninger
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Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.