Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 12
... equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 63
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they will be equal ; which was to be proved ...
Page 66
... at the greater distance from the centre . 1o . In the equal circles ACII and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
... at the greater distance from the centre . 1o . In the equal circles ACII and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
Page 67
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. and consequently , B M ED A K Ꭱ they will be equally dis- IV . ) ; tant from the ...
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. and consequently , B M ED A K Ꭱ they will be equally dis- IV . ) ; tant from the ...
Page 75
... : then will they be proportional to the arcs AB and FH . A DIO BF For , let the less angle FOH , be placed upon the greater angle ACB , SO that it shall take the position ACD . Then , it the proposition is not true , let BOOK III . 75.
... : then will they be proportional to the arcs AB and FH . A DIO BF For , let the less angle FOH , be placed upon the greater angle ACB , SO that it shall take the position ACD . Then , it the proposition is not true , let BOOK III . 75.
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Common terms and phrases
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
Popular passages
Page 101 - The area of a parallelogram is equal to the product of its base and altitude.
Page 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.
Page 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.
Page 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.
Page 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.
Page 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Page 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Page 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.
Page 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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.