## Elements of geometry and mensuration |

### From inside the book

Page 15

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**at the base of an isosceles triangle are equal to one another**" the converse would be " Shew that , if the angles at the base of a triangle are equal to one another , the triangle is isosceles " . ( 7 ) reductio ad absurdum ...### Other editions - View all

### Common terms and phrases

ABCD acres base bisect called centre chord circle circular circumference circumscribed compasses construction contained convenient curved describe diagonal diagram diameter difference distance divided division draw drawn edge equal exactly example expressed feet figure find the area fixed foot former four fraction given given circle given point given straight line greater ground half height Hence inches inscribed intersecting join length less magnitude marked means measure meet method nearly observed obtained opposite parallel parallelogram pass perimeter perpendicular placed plane plot portion PROB produced PROP proportional proposed radius ratio rectangle regular polygon remaining represent respectively result right angles scale shew shewn sides similar smaller square straight line subtends suppose surface taken taking triangle unit whole yards

### Popular passages

Page 32 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Page 19 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Page 27 - 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 32 - 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 43 - 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 17 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 22 - Theorem. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is greater than AB, make...

Page 192 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.

Page 126 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 20 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.