Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1865 - 444 Seiten |
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Seite 14
... Equivalent Magnitudes are those which , though they do not admit of coincidence when applied the one to the other , still have common measures , and are therefore numerically equal . 47. Similar Figures have equal angles , and the same ...
... Equivalent Magnitudes are those which , though they do not admit of coincidence when applied the one to the other , still have common measures , and are therefore numerically equal . 47. Similar Figures have equal angles , and the same ...
Seite 41
... equivalent , or equal in respect to area or sur- face . Let ABEC and ABDF be two C parallelograms on the same base AB , and between the same paral- lels AB and CD ; we are to prove that these two parallelograms are equal . E F D A B Now ...
... equivalent , or equal in respect to area or sur- face . Let ABEC and ABDF be two C parallelograms on the same base AB , and between the same paral- lels AB and CD ; we are to prove that these two parallelograms are equal . E F D A B Now ...
Seite 42
... equivalent . Let the two △ ' s ABE and ABF have the same base AB , and be be- tween the same parallels AB and EF ; then we are to prove that they C EF D are equal in surface . A B From B draw the line BD , par- allel to AF ; and from A ...
... equivalent . Let the two △ ' s ABE and ABF have the same base AB , and be be- tween the same parallels AB and EF ; then we are to prove that they C EF D are equal in surface . A B From B draw the line BD , par- allel to AF ; and from A ...
Seite 43
... equivalent parallelogram FH ; therefore , the ABD = the △ EFG , ( Ax . 7 ) . THEOREM XXX . If a triangle and a parallelogram are upon the same or equal bases , and between the same parallels , the triangle is equiva- lent to one half ...
... equivalent parallelogram FH ; therefore , the ABD = the △ EFG , ( Ax . 7 ) . THEOREM XXX . If a triangle and a parallelogram are upon the same or equal bases , and between the same parallels , the triangle is equiva- lent to one half ...
Seite 45
... equivalent to one half this rectangle , ( Th . 30 ) . Therefore , the area of the △ is measured by AB × AD , or one half the product of its base by its altitude . Hence the theorem ; the area of any plane triangle , etc. THEOREM XXXIV ...
... equivalent to one half this rectangle , ( Th . 30 ) . Therefore , the area of the △ is measured by AB × AD , or one half the product of its base by its altitude . Hence the theorem ; the area of any plane triangle , etc. THEOREM XXXIV ...
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Häufige Begriffe und Wortgruppen
2sin AB² ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.a cos.b cos.b cos.c Cosine Cotang diagonal diameter difference distance divided draw equal and parallel equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles Let ABC logarithm measured multiplied N.sine number of sides parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROB PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY straight line Tang tangent three angles three sides triangle ABC triangular prisms triedral angles Trigonometry vertex volume
Beliebte Passagen
Seite 318 - 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.
Seite 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Seite 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Seite 41 - 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.
Seite 96 - 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.
Seite 65 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Seite 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Seite 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.