## Elements of geometry and mensuration |

### From inside the book

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**intersecting**the former in the point C ; join the points A and C by the straight line AC ( POST . 1. ) , and B and C by the straight line BC ; then ABC shall be the equilateral triangle required . = B For since B and C are points in the ... Page 21

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**intersects*** an- other straight line , the vertical , or opposite , angles shall be equal to one another . Let the straight line AB**intersect**the straight line CD in the point E ; then LAEC = L BED , and AED = △ BEC . For , since CE ... Page 23

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**intersecting**line , as EFD ; then also AB shall be parallel to CD . For BEG . = LAEF ( 31 ) , . : LAEF = EFD , and .. AB , CD are parallel , as already proved . COR . 2. If the two interior angles on the same side of the**intersecting**... Page 28

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**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 may be shewn that BE = CE ; therefore AD , BC bisect ... Page 37

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**intersect**is equidistant from the three sides of the tri- angle . ( 22 ) Is it correct to speak of drawing a line from an angle ? The expression is found in Simson's Euclid ; what does it mean ? See definition of angle . ( 23 ) Simson ...### 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.