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 6
... quadrant . Each of the straight lines drawn from the centre to the cir- cumference is called a radius . Hence , all radii of the same circle are equal . F C B E A D A line passing through the centre and ter- minating in both directions ...
... quadrant . Each of the straight lines drawn from the centre to the cir- cumference is called a radius . Hence , all radii of the same circle are equal . F C B E A D A line passing through the centre and ter- minating in both directions ...
Page 7
... 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 of any particular angle , taken as the unit angle . The right ...
... 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 of any particular angle , taken as the unit angle . The right ...
Page 40
... quadrant . The straight line joining the extremities of an arc is called a chord . The chord is said to subtend the arc . Every chord corresponds always to two arcs , which together make up the entire circumference . It is the smaller ...
... quadrant . The straight line joining the extremities of an arc is called a chord . The chord is said to subtend the arc . Every chord corresponds always to two arcs , which together make up the entire circumference . It is the smaller ...
Page 48
... quadrant ; in the case of an angle equal to two right angles , the measuring arc is a semi - circumference . We sometimes regard the right angle as the unit angle , so that acute angles would all be less than 1 , and obtuse angles would ...
... quadrant ; in the case of an angle equal to two right angles , the measuring arc is a semi - circumference . We sometimes regard the right angle as the unit angle , so that acute angles would all be less than 1 , and obtuse angles would ...
Page 49
... quadrant . Each angle is a segment greater than a semicircle is acute , since half the included arc , which measures it , is less than a quadrant . Each angle in a segment less than a semicircle is obtuse , since half the included ...
... quadrant . Each angle is a segment greater than a semicircle is acute , since half the included arc , which measures it , is less than a quadrant . Each angle in a segment less than a semicircle is obtuse , since half the included ...
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Common terms and phrases
ABCD altitude apothem base bisect centre chord circle circumference circumscribed column cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation EXAMPLES exterior angles feet figures formula frustum Geom gives greater half Hence hypotenuse inches included angle intersection logarithmic sine measure multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular polygon respectively equal right angles right triangles right-angled triangle Scholium secant sector similar similar triangles sine slant height solid solve the triangle sphere spherical triangle square straight line subtract suppose surface tang tangent THEOREM three sides triangle ABC triangular prism volume
Popular passages
Page 35 - 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 17 - 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 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 182 - Every section of a sphere, made by a plane, is a circle.
Page 28 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Page 165 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.
Page 29 - ... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is.
Page 13 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.