Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1872 - 455 Seiten |
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Seite 76
... similar manner , it may be shown that the fourth term cannot be less than AD ; hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . • arc AD Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term cannot be less than AD ; hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . • arc AD Cor . 1. The intercepted arcs are ...
Seite 93
... SIMILAR ARCS , SECTORS , or SEGMENTS , in different circles , are those which correspond to equal angles at the centre . Thus , if the angles A and O are A equal , the arcs BFC and DGE are similar , the sectors BAC and DOE are similar ...
... SIMILAR ARCS , SECTORS , or SEGMENTS , in different circles , are those which correspond to equal angles at the centre . Thus , if the angles A and O are A equal , the arcs BFC and DGE are similar , the sectors BAC and DOE are similar ...
Seite 113
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
Seite 114
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they will be similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they will be similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
Seite 115
... similar . For , on BA lay off BG equal to ED ; off BH equal to EF , and draw GH . Then , because BG is equal to DE , and BH to EF , we have , A on BC lay B E BA : BG :: BC : BH ; D hence , GH is parallel to AC ( P. XVI . ) ; and ...
... similar . For , on BA lay off BG equal to ED ; off BH equal to EF , and draw GH . Then , because BG is equal to DE , and BH to EF , we have , A on BC lay B E BA : BG :: BC : BH ; D hence , GH is parallel to AC ( P. XVI . ) ; and ...
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder decimal denote diameter difference distance divided draw drawn edges equal to AC Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle pole polyedral angle polyedron prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triedral angle upper base vertex vertices volume whence
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Seite 101 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 92 - PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob.
Seite 48 - 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.
Seite 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Seite 106 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Seite 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Seite 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Seite 30 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has the greater included angle.
Seite 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 156 - DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as the squares of their radii.