## Euclid, book i., propositions i. to xxvi., with exercises and alternative proofs [by T. Dalton].1877 |

### From inside the book

Results 1-5 of 14

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**equal**to the less . Let AB and**CD**be the two given straight lines , of which AB is the greater ; it is required to cut off from AB the greater , a part**equal**to OD the less . с E F B Construction . From A draw the straight line AE ... Page 11

... CD is equal to AE ; ( const . ) therefore AF and CD are each of them equal to AE , and therefore AF and CD are equal to each other . ( ax . 1 ) Wherefore from AB the greater of two straight lines , a part AF has been cut off

... CD is equal to AE ; ( const . ) therefore AF and CD are each of them equal to AE , and therefore AF and CD are equal to each other . ( ax . 1 ) Wherefore from AB the greater of two straight lines , a part AF has been cut off

**equal to**... Page 12

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**equal**to the side DF , and the included angle BAC**equal**to the included angle EDF , then shall the base BC be**equal**...**CD**from its middle point B. Shew that AC and AD are of**equal**length . 3. The vertical angle BAC of an isosceles ... Page 13

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**equal**parts ) by a straight line AD ( D being outside the line BC ) ; shew that DBC is an isosceles triangle . 4 ...**CD**. 8. The triangle formed by joining the middle points of the sides of an equilateral triangle is also equilateral . 9. Page 17

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**equal**to the side AB . A B Construction . If AC is not**equal**to AB , one of them must be greater than the other ; suppose then that AB is the greater , and from BA the greater cut off BD**equal**to CA the less ; ( prop . 3 ) join**CD**...### Other editions - View all

Euclid, Book I., Propositions I. to XXVI., with Exercises and Alternative ... Euclides No preview available - 2016 |

Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides No preview available - 2023 |

Euclid, Book I., Propositions I. to Xxvi., With Exercises and Alternative ... Euclides No preview available - 2023 |

### Common terms and phrases

A'EF AB is equal AC is equal ACD is greater adjacent angles angle ABC angle ACB angle BAC angle BCD angle BDC greater angle contained angle DEF angle DFE angle EDF angle equal bisects the angle centre circumference constr DEF are equal Demonstration describe the circle draw a straight equal angles equal sides equal to CD equidistant equilateral triangle Euclid exterior angle Find a point four-sided figure given line given point given straight line greater than BC interior opposite angle intersect isosceles triangle less Let ABC line with BC middle point opposite sides perpendiculars let fall point G position be named produced prop PROPOSITION Q.E.D. Exercises quadrilateral right angles shew shewn side AC sides equal straight line drawn take any point THEOREM third side triangle ABC triangle DEF triangles be equal unequal vertical angle

### Popular passages

Page 39 - IF two triangles have two sides of the one equal to two sides of the...

Page 25 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Page 4 - 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 7 - If a straight line meet 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 7 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.

Page 36 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.

Page 37 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.

Page 18 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.

Page 29 - If, at a point in a straight line, two other straight lines, upon 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. At the point B in the straight line AB, let the two straight lines...

Page 3 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.