## Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |

### From inside the book

Results 1-5 of 68

Page 12

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**ABC**shall be an equilateral**triangle**. Because the point A is the centre of the circle BCD , AC is equal to AB ; and because the point B is the cen- 12 De tre of the circle ACE , BC is equal to BA : But it has been proved that CA is ... Page 14

... 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 the angle DEF , and the angle ACB to DFE . B CE For , if the

... 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 the angle DEF , and the angle ACB to DFE . B CE For , if the

**triangle ABC**be applied to DEF ... Page 15

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**triangle**are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let**ABC**be an isosceles**triangle**, of which the side AB is equal to AC , and let the straight lines AB ... Page 16

... ABC is equal † to the remaining +3 Ax . angle ACB , which are the angles at the base of the

... ABC is equal † to the remaining +3 Ax . angle ACB , which are the angles at the base of the

**triangle ABC**: and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base ... Page 18

... triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases ...

... triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases ...

**triangle ABC**be applied to DEF , so that the point B D G CE B be on E , and the straight line BC upon EF ; the point ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore

### Popular passages

Page 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Page 105 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Page 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Page 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Page 41 - 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 172 - 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 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

Page 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.