Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 16
... 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 . A For since B and C are points in the ...
... 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 . A For since B and C are points in the ...
Page 21
... 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 = LBED , and AED = ‹ BEC . For , since CE ...
... 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 = LBED , and AED = ‹ BEC . For , since CE ...
Page 23
... intersecting line , as ¿ EFD ; then also AB shall be parallel to CD . For BEGLAEF ( 31 ) , .. < AEF = ¿ EFD , and .. AB , CD are parallel , as already proved . COR . 2. If the two interior angles on the same side of the intersecting ...
... intersecting line , as ¿ EFD ; then also AB shall be parallel to CD . For BEGLAEF ( 31 ) , .. < AEF = ¿ 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
... intersect in E ; then , since L ABE = = 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 ...
... intersect in E ; then , since L ABE = = 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
... 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 ...
... 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 ...
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Common terms and phrases
ABCDEF angular points base bisect centre chain chord circular circumference circumscribed circumscribing circle compasses cone construction cubic curved cylinder describe a circle diagonal diameter distance divided draw a straight drawn edge equal angles equal arcs equilateral triangle feet find the area foot frustum given angle given circle given line given point given ratio given straight line given triangle greater height Hence hexagon inches inscribed instrument intersecting length Let ABCD magnitude measure meet number of sides opposite angle parallelogram parallelopiped perimeter perpendicular plane surface points of division prism PROB produced PROP proportional Protractor radii radius rectangle rectangle contained regular polygon right angles ruler scale segment semi-circle shew shewn similar triangles square of AB square of AC subtends suppose tangent trapezium triangle ABC unit 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 16 - 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 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 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 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 223 - 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 128 - 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.