Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration : Accompanied with All the Necessary Logarithmic and Trigonometric TablesD. Appleton, 1860 - 443 σελίδες |
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Σελίδα vii
... formulas ..... 56 CHAPTER VI . Solution of spherical right triangles ... 72 Of the circular parts .. 71 Examples for practice . 92 CHAPTER VII . Mensuration of surfaces ..... 93 1 CHAPTER VIII . Mensuration of solids .. 109 . PART FIRST ...
... formulas ..... 56 CHAPTER VI . Solution of spherical right triangles ... 72 Of the circular parts .. 71 Examples for practice . 92 CHAPTER VII . Mensuration of surfaces ..... 93 1 CHAPTER VIII . Mensuration of solids .. 109 . PART FIRST ...
Σελίδα 86
... formula , we shall have 0 D BD2 AB2 + AD2 + 2AB × AD . = Adding now , to each member of this , CD2 , and observing that BD2 + CD2 = BC2 , and also that AD2 + CD2 = AC2 , we shall obtain BC2AB + AC2 + 2AB × AD . THEOREM XVI . In any ...
... formula , we shall have 0 D BD2 AB2 + AD2 + 2AB × AD . = Adding now , to each member of this , CD2 , and observing that BD2 + CD2 = BC2 , and also that AD2 + CD2 = AC2 , we shall obtain BC2AB + AC2 + 2AB × AD . THEOREM XVI . In any ...
Σελίδα 87
... formula , we sha.1 have BD2 AB2 + AD2-2AB X AD . = Adding to each member of this DC , and observing that BD2 + CD2 = BC2 , and also that AD2 + DC2 = AC2 , we shall obtain BC2 AB2 + AC2-2AB X AD . = = This result will hold good even when ...
... formula , we sha.1 have BD2 AB2 + AD2-2AB X AD . = Adding to each member of this DC , and observing that BD2 + CD2 = BC2 , and also that AD2 + DC2 = AC2 , we shall obtain BC2 AB2 + AC2-2AB X AD . = = This result will hold good even when ...
Σελίδα 98
... that , of the three similar polygons , the polygon con- structed on the hypotenuse is equivalent to the sum of the poly- gons constructed on the sides containing the right angle . Scholium . The algebraic formulas , ( p + q 98 GEOMETRY .
... that , of the three similar polygons , the polygon con- structed on the hypotenuse is equivalent to the sum of the poly- gons constructed on the sides containing the right angle . Scholium . The algebraic formulas , ( p + q 98 GEOMETRY .
Σελίδα 99
... formulas , ( p + q ) 2 = p2 + q2 + 2pq , ( p − q ) 2 = p2 + q2 — 2pq , - which have been made the bases of Theorems XV . and XVI . , and the other well - known formula , ( p + q ) × ( p − q ) = p2 — q2 , - being translated into ...
... formulas , ( p + q ) 2 = p2 + q2 + 2pq , ( p − q ) 2 = p2 + q2 — 2pq , - which have been made the bases of Theorems XV . and XVI . , and the other well - known formula , ( p + q ) × ( p − q ) = p2 — q2 , - being translated into ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 113 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 31 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 112 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Σελίδα 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.
Σελίδα 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'.
Σελίδα 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.
Σελίδα 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.
Σελίδα 174 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Σελίδα 107 - ... similar figures are to each other as the squares of their homologous sides.
Σελίδα 180 - Every section of a sphere, made by a plane, is a circle.