## Elements of geometry and mensuration |

### From inside the book

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**bisect**a given angle , that is , to divide it into two equal angles . Let BAC be the given angle ; it is required to**bisect**it . In AB take any point D , and with centre A and radius AD describe an arc of a circle cutting AC in the ... Page 18

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**Bisect**the angle BAC by the straight line AD ( 25 ) , D being the point where AD meets the base BC . Then , since AB AC , and △ BAD = L CAD , we have two tri- angles ABD , ACD , in which the two sides BA , AD are equal to the two sides ... Page 20

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**bisect**ECF by the line CG , meeting AB in G. Then CG shall be perpendicular to AB . - For CE CF ( 16 ) , and 4 ECG = < FCG , by construc- tion , .. in the triangles ECG , FCG , EC , CG are equal to FC , CG , each to each , and ECG ... Page 22

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**Bisect**the side AC in the point E ( 27 ) , join BE , produce it to F , making EF equal to EB B D ( by describing a ...**bisecting**BC in G , joining AG , and proceeding as before , that ACD is greater than ABC . L 33. PROP . XI . The ... Page 28

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**bisect**each other . = 4 Join AD , and let BC , AD , intersect in E ; then , since ABE = 2 DCE , and △ BAE = △ CDE , and side AB side CD , the triangles ABE , CDE , are equal in all respects ( 39 ) ; side AE = side DE . Similarly it ...### Other editions - View all

### Common terms and phrases

ABCDEF acres base bisect breadth centre chain chord circular circum circumference circumscribing circle compasses construction contained continued fraction curved decimal Diagonal Scale diagram diameter distance divided draw drawn edge equilateral triangle find the area find the length fraction frustum given angle given circle given line given point given straight line given triangle half height Hence hexagon inscribed instrument intersecting join Let ABCD lineal unit magnitude meet multiplied number of equal number of sides number of units opposite angle parallelogram perimeter perpendicular plane surface plot points of division PROB produced PROP proportional Protractor radii radius ratio rectangle rectangular regular polygon represent right angles shew shewn similar similar triangles square feet square foot square inches straight edge subtends suppose trapezium triangle ABC vernier vertex 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.