Elements of Geometry and Trigonometry: With Applications in Mensuration |
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Page 10
... , the angle CAB . We may , however , say simply , the angle A. 20. One line is said to be perpendicular to another when it inclines no more to the one side than to the other 513 DI BOOK I. Definitions . ' The two angles 10 GEOMETRY .
... , the angle CAB . We may , however , say simply , the angle A. 20. One line is said to be perpendicular to another when it inclines no more to the one side than to the other 513 DI BOOK I. Definitions . ' The two angles 10 GEOMETRY .
Page 11
... perpendicular to each other , the angles which they form are called right angles . Thus , DBA and DBC are called right angles . 22. An acute angle is less than a right angle . Thus , DBC is an acute angle . 23. An obtuse angle is ...
... perpendicular to each other , the angles which they form are called right angles . Thus , DBA and DBC are called right angles . 22. An acute angle is less than a right angle . Thus , DBC is an acute angle . 23. An obtuse angle is ...
Page 12
... to the horizon , or to the water level , are called horizontal lines . 34. Lines which are perpendicular to the horizon , or to the water level , are called vertical lines . Definitions . OF PLANE FIGURES . 35. A Plane Figure 12 GEOMETRY .
... to the horizon , or to the water level , are called horizontal lines . 34. Lines which are perpendicular to the horizon , or to the water level , are called vertical lines . Definitions . OF PLANE FIGURES . 35. A Plane Figure 12 GEOMETRY .
Page 16
... perpendicular to the base . AXIOMS . 1. Things which are equal to the same thing are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3. If equals be taken from equals , the remainders will be equal . 4 ...
... perpendicular to the base . AXIOMS . 1. Things which are equal to the same thing are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3. If equals be taken from equals , the remainders will be equal . 4 ...
Page 26
... ) : and hence , the alternate angles AEF and EFD are equal . Cor . If a line be perpendicular to one of two parallel lines , it will also be per- pendicular to the other Of Parallel Lines . THEOREM XIII . 1 Conversely , 26 GEOMETRY .
... ) : and hence , the alternate angles AEF and EFD are equal . Cor . If a line be perpendicular to one of two parallel lines , it will also be per- pendicular to the other Of Parallel Lines . THEOREM XIII . 1 Conversely , 26 GEOMETRY .
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Common terms and phrases
adjacent angles allel alternate angles altitude angle ACB angles equal base multiplied bisect called centre chains chord circle whose diameter circumference cone consequently convex surface Cosine Cosine D Cotang cubic cylinder decimal diagonal dicular distance divided draw drawn equal Bk equal Th equal to half equivalent feet figure find the area frustum half the arc half the product hence horizontal hypothenuse inches included angle inscribed intersect Let ABC logarithm lower base M.
M. Sine measured by half Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane prism PROBLEM proportion quadrilateral radius ratio rectangle regular polygon Required the area rhombus right angled triangle right angles Th segment side AC similar similar triangles slant height solidity sphere straight line suppose Tang tangent THEOREM triangle ABC yards
Popular passages
Page 48 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 12 - 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, etc.
Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 85 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 198 - To find the area of a trapezoid. RULE. Multiply the sum of the parallel sides by the perpendicular distance between them, and then divide the product by two : the quotient will be the area (Bk.
Page 159 - In every plane triangle there are six parts : three sides and three angles. These parts are so related to each other, that when one side and any two other parts are given, the remaining ones can be obtained, either by geometrical construction or by trigonometrical computation.
Page 187 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Page 79 - 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 119 - If a cone be cut by a plane parallel to the base, the section will be a circle.