Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 12
... difference is the area ABC . B D Again , if area ABC = area BCD , then area ACD is double of the area ABC ; and area ABC - half of area ACD . Angles likewise are magnitudes which may be added , subtracted , & c . Thus , ACB + 4 BCD LACD ...
... difference is the area ABC . B D Again , if area ABC = area BCD , then area ACD is double of the area ABC ; and area ABC - half of area ACD . Angles likewise are magnitudes which may be added , subtracted , & c . Thus , ACB + 4 BCD LACD ...
Page 13
... difference between the angle ABC and the triangle ABC . ( 13 ) By what names are triangles distinguished ac- cording to their form ? Exhibit a triangle of each sort . ( 14 ) Does the magnitude of an angle depend upon the magnitude of ...
... difference between the angle ABC and the triangle ABC . ( 13 ) By what names are triangles distinguished ac- cording to their form ? Exhibit a triangle of each sort . ( 14 ) Does the magnitude of an angle depend upon the magnitude of ...
Page 14
... difference between an angle , and a corner ? What is the geometrical name for the latter ? EXPLANATION OF TECHNICAL TERMS USED IN GEOMETRY . ( 1 ) To ' describe ' a certain geometrical figure , means to construct , or trace , it on a ...
... difference between an angle , and a corner ? What is the geometrical name for the latter ? EXPLANATION OF TECHNICAL TERMS USED IN GEOMETRY . ( 1 ) To ' describe ' a certain geometrical figure , means to construct , or trace , it on a ...
Page 26
... shewn that AB + BC is greater than AC , and AC + AB greater than BC . COR . Hence , also , the difference between any two sides is less than the third side . 39. PROP . XVII . If two triangles have two 26 GEOMETRY AS A SCIENCE .
... shewn that AB + BC is greater than AC , and AC + AB greater than BC . COR . Hence , also , the difference between any two sides is less than the third side . 39. PROP . XVII . If two triangles have two 26 GEOMETRY AS A SCIENCE .
Page 38
... difference betwixt the two ? ( 24 ) Shew that the straight line drawn from the vertex of the right angle in a right - angled triangle to the middle point of the hypothenuse is equal to half the hypothenuse . ( 25 ) Explain what is meant ...
... difference betwixt the two ? ( 24 ) Shew that the straight line drawn from the vertex of the right angle in a right - angled triangle to the middle point of the hypothenuse is equal to half the hypothenuse . ( 25 ) Explain what is meant ...
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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.