## Elements of geometry, based on Euclid, book i |

### From inside the book

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**opposite sides**equal to one another , but all its**sides**are not equal , nor its angles right angles . 34. Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . 35. A ... Page 12

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**sides are opposite**. Or , If two sides and the contained angle of one triangle be re- spectively equal to those of another , the triangles are equal in every respect . Let ABC , DEF be two triangles which have The two sides AB , AC ... Page 13

Edward Atkins. And the other angles to which the equal

Edward Atkins. And the other angles to which the equal

**sides are opposite**, shall be equal , each to each , viz . , the angle ABC to the angle DEF , and the angle ACB to the angle DFE . - PROOF . For if the triangle ABC be applied to ... Page 14

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**sides are opposite**, viz . , the angle ACF to the angle ABG , and the angle AFC to the angle AGB ( I. 4 ) . And because the whole AF is equal to the whole AG , of which the parts AB , AC , are equal ( Hyp . ) , The remainder BF is equal ... Page 15

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**sides**also which subtend , or are**opposite**to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB . The**side**AB shall be equal to the**side**AC . For if AB be not equal to ...### Other editions - View all

### Common terms and phrases

ABC is equal adjacent angles alternate angles angle ABC angle BAC angle BCD angle contained angle EDF angle EGB angle GHD angles BGH angles CBE angles equal bisect centre cloth Const describe the circle diagonal equal sides equal to BC equal triangles equilateral triangle exterior angle Fcap four right angles GHD Ax given point given rectilineal angle given straight line given triangle gram HENRY EVERS interior and opposite isosceles triangle join less Let ABC LL.D meet opposite angles parallel straight lines parallel to BC parallelogram ABCD perpendicular Post 8vo PROOF PROOF.-Because Q. E. D. Proposition rectilineal figure remaining angle right angles Ax side BC sides are opposite sides equal square described square GB third angle trapezium triangle ABC triangle DEF WILLIAM COLLINS

### Popular passages

Page 23 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 33 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.

Page 43 - Parallelograms upon the same base, and between the same parallels, are equal to one another.

Page 15 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall also be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC...

Page 11 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.

Page 37 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 41 - ... together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 15 - J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.

Page 55 - IF the square described upon one of 'the sides of a triangle be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Page 24 - If, at a point in a straight line, two other straight lines, on the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.