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 Corrected |
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Page 15
... 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 ABC to ...
... 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 ABC to ...
Page 16
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to ...
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to ...
Page 18
... angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF ...
... angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF ...
Page 22
... angle CBA be equal to ABD , each of them is a A D B E D B A C right ( def . 10. ) angle ; but , if not , from the ... ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been ...
... angle CBA be equal to ABD , each of them is a A D B E D B A C right ( def . 10. ) angle ; but , if not , from the ... ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been ...
Page 23
... ABC , ABD are 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 ( 3. Ax . ) to the re- maining angle ABD ...
... ABC , ABD are 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 ( 3. Ax . ) to the re- maining angle ABD ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw 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 multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition 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 third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 81 - The angles in the same segment of a circle are equal to one another.
Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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.
Page 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.
Page 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.
Page 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.
Page 22 - ANY two angles of a triangle are together less than two right angles.
Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Page 24 - Any two sides of a triangle are together greater than the third side.