Manual of Geometry and Conic Sections: With Applications to Trigonometry and Mensuration |
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Page 7
... line ; if two lines intersect , that which is common to both is called a point . General Definitions . 2. A magnitude is anything that can be measured , that ... line . A It is assumed that one straight line , and only GEOMETRY INTRODUCTION.
... line ; if two lines intersect , that which is common to both is called a point . General Definitions . 2. A magnitude is anything that can be measured , that ... line . A It is assumed that one straight line , and only GEOMETRY INTRODUCTION.
Page 8
... line is a line made up of straight lines lying in different direc- tions ; thus , ACDE is a broken line . 9. A curved line , or a curve , is a line whose direction changes at every point ; thus , ACD is a curved line . When the term ...
... line is a line made up of straight lines lying in different direc- tions ; thus , ACDE is a broken line . 9. A curved line , or a curve , is a line whose direction changes at every point ; thus , ACD is a curved line . When the term ...
Page 10
... straight line is the shortest path between two points . Postulates . 1o . A straight line can be drawn through any two points . 2o . A straight line can be prolonged to any extent . 3o . A straight line can be constructed equal to a given ...
... straight line is the shortest path between two points . Postulates . 1o . A straight line can be drawn through any two points . 2o . A straight line can be prolonged to any extent . 3o . A straight line can be constructed equal to a given ...
Page 16
... line , and lying on the same side of that line , is equal to two right angles . For , the sum of the angles AOC ... straight line . Let the sum of AOC and COP be equal to 16 MANUAL OF GEOMETRY .
... line , and lying on the same side of that line , is equal to two right angles . For , the sum of the angles AOC ... straight line . Let the sum of AOC and COP be equal to 16 MANUAL OF GEOMETRY .
Page 18
... straight line . ( P. 4. ) . But this is impossible , because only one straight line can be drawn through two points ; hence , the supposition that a second . line can be drawn through D perpendicular to PA is false ; DA is therefore the ...
... straight line . ( P. 4. ) . But this is impossible , because only one straight line can be drawn through two points ; hence , the supposition that a second . line can be drawn through D perpendicular to PA is false ; DA is therefore the ...
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Common terms and phrases
ACD and PQR ACDE-K altitude angles are equal apothem base and altitude bisectrix bisects centre chord circle OA circumscribed coincide cone conic surface consequently corresponding Cosine Cotang curve denoted diameter distance divide draw ellipse equal to AC equally distant find the area formula frustum given line given point greater hence hyperbola hypothenuse included angle intersect lateral surface less Let ACD logarithm lower base mantissa multiplied number of sides opposite parabola parallelogram parallelopipedon perimeter perpendicular plane KL prolongation PROPOSITION proved pyramid quadrant radii radius rectangle regular inscribed regular polygon right angles right-angled triangle Scho secant segments similar slant height sphere spherical excess spherical triangle square straight line subtracting Tang tangent THEOREM transverse axis triangle ACD triangles are equal triangular prism triedral angle upper base vertex volume
Popular passages
Page 72 - In any proportion, the product of the means is equal to the product of the extremes.
Page 72 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Page 19 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Page 273 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 108 - 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 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Page 36 - The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Page 104 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Page 36 - ... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles...
Page 70 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.