Plane and Solid GeometryGinn, 1904 - 473 σελίδες |
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Αποτελέσματα 1 - 5 από τα 46.
Σελίδα 135
... proportional to a , b , and c in the proportion abc : d . 326. The quantities a , b , c , d , e , are said to be in ... proportional between the other two , and the third is called the third proportional to the other two . Thus , in the ...
... proportional to a , b , and c in the proportion abc : d . 326. The quantities a , b , c , d , e , are said to be in ... proportional between the other two , and the third is called the third proportional to the other two . Thus , in the ...
Σελίδα 136
... proportional between two quantities is equal to the square root of their product . Let a : b = : b : c . Then b2 = ac . § 327 Whence , extracting the square root , b = √ac . Q. E. D. PROPOSITION III . THEOREM . 329. If the product of ...
... proportional between two quantities is equal to the square root of their product . Let a : b = : b : c . Then b2 = ac . § 327 Whence , extracting the square root , b = √ac . Q. E. D. PROPOSITION III . THEOREM . 329. If the product of ...
Σελίδα 143
... proportional . Draw AN to CD . Then A C AL = CG , LM : = GK , MN FL G = KD . § 180 1 Now AH : AM = AF : AL : H M = FH : LM K = HB : MN . § 343 B N D Or AF : CGFH : GK = HB : KD . PROPOSITION XIV . THEOREM . 345. If a straight line THE ...
... proportional . Draw AN to CD . Then A C AL = CG , LM : = GK , MN FL G = KD . § 180 1 Now AH : AM = AF : AL : H M = FH : LM K = HB : MN . § 343 B N D Or AF : CGFH : GK = HB : KD . PROPOSITION XIV . THEOREM . 345. If a straight line THE ...
Σελίδα 144
... proportional to 91 , 65 , and 133 . Ex . 247. Find the mean proportional between 39 and 351 . Ex . 248. Find the third proportional to 54 and 3 . $ 47 Const . Q. E. D. 346. If a given line AB is divided at M 144 BOOK III . PLANE GEOMETRY .
... proportional to 91 , 65 , and 133 . Ex . 247. Find the mean proportional between 39 and 351 . Ex . 248. Find the third proportional to 54 and 3 . $ 47 Const . Q. E. D. 346. If a given line AB is divided at M 144 BOOK III . PLANE GEOMETRY .
Σελίδα 146
... proportional to the adjacent sides . E A M B Let CM bisect the angle C of the triangle CAB . To prove that MA : MB ... proportionally ) . LACM CAE , = ( being alt . - int . ≤ of || lines ) ; LBCM = LCEA , ( being ext . - int . 4 of ...
... proportional to the adjacent sides . E A M B Let CM bisect the angle C of the triangle CAB . To prove that MA : MB ... proportionally ) . LACM CAE , = ( being alt . - int . ≤ of || lines ) ; LBCM = LCEA , ( being ext . - int . 4 of ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCDE AC² altitude apothem axis bisector bisects called centre chord circumference circumscribed coincide common construct curve denote diagonals diameter dihedral angles distance divided draw ellipse equidistant equilateral triangle equivalent face angles feet Find the area Find the locus frustum given circle given line given point given straight line given triangle greater Hence homologous homologous sides hypotenuse inches intersection lateral area lateral edges length limit middle point number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism prismatoid Proof prove Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon regular pyramid respectively right angle right circular right triangle secant segments similar slant height sphere spherical polygon spherical triangle square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangular prism trihedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 44 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 276 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.
Σελίδα 52 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 43 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.
Σελίδα 193 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Σελίδα 362 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 171 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Σελίδα 73 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Σελίδα 385 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.
Σελίδα 77 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.