Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult Classes |
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Page 1
... Hence it is necessarily much concerned with the terms ' length ' , ' breadth ' , ' height ' , ' depth ' , ' thickness ' , ' area ' , ' content ' , or ' volume ' ; and that which does not possess some one or more of these properties is ...
... Hence it is necessarily much concerned with the terms ' length ' , ' breadth ' , ' height ' , ' depth ' , ' thickness ' , ' area ' , ' content ' , or ' volume ' ; and that which does not possess some one or more of these properties is ...
Page 2
... hence is required a sort of geometrical language in the first onset , which must be learnt from the following Definitions : - 3. We measure a distance by a ' line ' ; so that a line will represent any one of the dimensions length ...
... hence is required a sort of geometrical language in the first onset , which must be learnt from the following Definitions : - 3. We measure a distance by a ' line ' ; so that a line will represent any one of the dimensions length ...
Page 3
... the carpet never enters into our consideration , but only the length and breadth . Hence the expression ' superficial measure ' is always understood to exclude thickness . Thus , for instance , 1-2 DEFINITIONS AND FIRST PRINCIPLES . 3.
... the carpet never enters into our consideration , but only the length and breadth . Hence the expression ' superficial measure ' is always understood to exclude thickness . Thus , for instance , 1-2 DEFINITIONS AND FIRST PRINCIPLES . 3.
Page 9
... Hence it is plain , that a circle may be traced by means of a string , one end of which is kept fixed in a certain point as the centre , while the other is made to revolve and trace out the circumference , the string being kept ...
... Hence it is plain , that a circle may be traced by means of a string , one end of which is kept fixed in a certain point as the centre , while the other is made to revolve and trace out the circumference , the string being kept ...
Page 10
... Hence the two straight lines AB , and CD , are equal to one another , if , when CD is placed upon AB , so that the point C is upon A and CD upon AB , the point D is found to coincide with the point B. C D In like manner two areas are ...
... Hence the two straight lines AB , and CD , are equal to one another , if , when CD is placed upon AB , so that the point C is upon A and CD upon AB , the point D is found to coincide with the point B. C D In like manner two areas are ...
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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.