Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1865 - 444 Seiten |
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Seite 26
... ABCD be a parallelo- gram . We are to prove that the sum of the angles A , B , C and D , is equal to four right angles , or to 360 ° . D C A B Because AD and BC are parallel lines , and AB inter- sects them , the two interior angles A ...
... ABCD be a parallelo- gram . We are to prove that the sum of the angles A , B , C and D , is equal to four right angles , or to 360 ° . D C A B Because AD and BC are parallel lines , and AB inter- sects them , the two interior angles A ...
Seite 31
... ABCD is a quadrilateral , the sum of the four interior angles is four right angles ( Prop . 13 ) , and because the angles ABC and ADC are each right angles , the sum of the angles BAD , BCD is two right angles . But the sum of the ...
... ABCD is a quadrilateral , the sum of the four interior angles is four right angles ( Prop . 13 ) , and because the angles ABC and ADC are each right angles , the sum of the angles BAD , BCD is two right angles . But the sum of the ...
Seite 39
... ABCD be a parallelogram . D C Then we are to show that AB = DC , AD = BC , A = C , and ADC = ABC . Draw a diagonal , as BD ; now , be- A cause AB and DC are parallel , the al- B ternate angles ABD and BDC are equal , ( Th . 6 ) . For ...
... ABCD be a parallelogram . D C Then we are to show that AB = DC , AD = BC , A = C , and ADC = ABC . Draw a diagonal , as BD ; now , be- A cause AB and DC are parallel , the al- B ternate angles ABD and BDC are equal , ( Th . 6 ) . For ...
Seite 40
... ABCD be any quadrilateral ; on the supposition that AD = BC , and AB = DC , we are to prove that AD is parallel to BC , and AB parallel to DC . D C B Draw the diagonal BD ; we now A have two triangles , ABD and BCD , which have the side ...
... ABCD be any quadrilateral ; on the supposition that AD = BC , and AB = DC , we are to prove that AD is parallel to BC , and AB parallel to DC . D C B Draw the diagonal BD ; we now A have two triangles , ABD and BCD , which have the side ...
Seite 42
... ABCD and EFGH , be two D parallelograms on equal bases , AB and EF , and between the same parallels , AF and DG ... ABCD , ( Th . 27 ) ; and if we turn the whole figure over , the two parallelo- grams , GHEF and GHAB , will stand ...
... ABCD and EFGH , be two D parallelograms on equal bases , AB and EF , and between the same parallels , AF and DG ... ABCD , ( Th . 27 ) ; and if we turn the whole figure over , the two parallelo- grams , GHEF and GHAB , will stand ...
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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.