Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration : Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page v
... perpendicular and oblique lines 20 Of parallel lines 24 Of triangles ... 28 Of quadrilaterals .. 33 Additional Theorems of triangles 37 SECOND BOOK , Definitions .... Of chords , secants , and tångents 40 42 Of the measure of angles Of ...
... perpendicular and oblique lines 20 Of parallel lines 24 Of triangles ... 28 Of quadrilaterals .. 33 Additional Theorems of triangles 37 SECOND BOOK , Definitions .... Of chords , secants , and tångents 40 42 Of the measure of angles Of ...
Page 7
... perpendicular to the other . between the radii is less than a quadrant , the angle is called acute . When the arc is greater than a quadrant , the angle is called obtuse . The magnitude of an angle may be estimated or measured by means ...
... perpendicular to the other . between the radii is less than a quadrant , the angle is called acute . When the arc is greater than a quadrant , the angle is called obtuse . The magnitude of an angle may be estimated or measured by means ...
Page 9
... or crosses another , so as to make the adjacent angles equal , each of these angles is called a Right angle , and the lines are said to be perpendicular to each other . • XIII . An Acute angle is one which is FIRST BOOK Definitions.
... or crosses another , so as to make the adjacent angles equal , each of these angles is called a Right angle , and the lines are said to be perpendicular to each other . • XIII . An Acute angle is one which is FIRST BOOK Definitions.
Page 11
... extent . III . That a straight line may be bisected or halved . IV . That from a point , either within or without a straight line , a perpendicular may be drawn to the line . IV . A postulate is a proposition , the truth FIRST BOOK . 13.
... extent . III . That a straight line may be bisected or halved . IV . That from a point , either within or without a straight line , a perpendicular may be drawn to the line . IV . A postulate is a proposition , the truth FIRST BOOK . 13.
Page 14
... perpendicular to AB , we see that the angle AFC exceeds the right angle AFG , by the angle CFG ; while the angle BFC is less than the right angle BFG by the same angle CFG . Hence , the sum of AFC , BFC is equal to two right angles ...
... perpendicular to AB , we see that the angle AFC exceeds the right angle AFG , by the angle CFG ; while the angle BFC is less than the right angle BFG by the same angle CFG . Hence , the sum of AFC , BFC is equal to two right angles ...
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Common terms and phrases
a+b+c ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum given angle given line gives greater half hence hypotenuse inches included angle inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume
Popular passages
Page 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - 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 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 15 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 107 - ... similar figures are to each other as the squares of their homologous sides.
Page 180 - Every section of a sphere, made by a plane, is a circle.