Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 15
... Shew that , if the angles at the base of a triangle are equal to one another , the triangle is isosceles " . ( 7 ) ' reductio ad absurdum ' , ( reducing to an absurdity ) , is a particular mode of demonstration often used by Euclid . It ...
... Shew that , if the angles at the base of a triangle are equal to one another , the triangle is isosceles " . ( 7 ) ' reductio ad absurdum ' , ( reducing to an absurdity ) , is a particular mode of demonstration often used by Euclid . It ...
Page 36
... Shew that only one straight line can be drawn perpendicular to a given straight line from a given point without it . ( 9 ) Shew that the perpendicular is the shortest of all lines from a given point to a given straight line . Of all ...
... Shew that only one straight line can be drawn perpendicular to a given straight line from a given point without it . ( 9 ) Shew that the perpendicular is the shortest of all lines from a given point to a given straight line . Of all ...
Page 37
... shew that these straight lines are at right angles to one another . ( 11 ) Shew that any point in the straight line bi- secting an angle is equidistant from the two straight lines forming the angle . ( 12 ) Shew that any side of a ...
... shew that these straight lines are at right angles to one another . ( 11 ) Shew that any point in the straight line bi- secting an angle is equidistant from the two straight lines forming the angle . ( 12 ) Shew that any side of a ...
Page 38
... 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 by the square of a line . Is the ...
... 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 by the square of a line . Is the ...
Page 50
... Shew that the circumferences of circles which have the same centre cannot cut each other . ( 6 ) If the circumference of a circle be divided into four equal arcs , shew that the chords of any two of them , which are adjacent , are at ...
... Shew that the circumferences of circles which have the same centre cannot cut each other . ( 6 ) If the circumference of a circle be divided into four equal arcs , shew that the chords of any two of them , which are adjacent , are at ...
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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.