Elements of GeometryHarper & brothers, 1896 - 540 sider |
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Resultat 1-5 av 65
Side 60
... square is a rectangle whose sides are all equal . 115. Def . - A diagonal of a quadrilateral is a straight line joining opposite vertices . PROPOSITION XXXV . THEOREM 116. A diagonal of a parallelogram divides it into two equal ...
... square is a rectangle whose sides are all equal . 115. Def . - A diagonal of a quadrilateral is a straight line joining opposite vertices . PROPOSITION XXXV . THEOREM 116. A diagonal of a parallelogram divides it into two equal ...
Side 87
... whole number of times in each . Thus it can be proved that the circumference and diameter of a circle are incommensurable ; also the side and diagonal of a square . LIMITS 183. Def . — A constant quantity is one BOOK II 87 MEASUREMENT.
... whole number of times in each . Thus it can be proved that the circumference and diameter of a circle are incommensurable ; also the side and diagonal of a square . LIMITS 183. Def . — A constant quantity is one BOOK II 87 MEASUREMENT.
Side 142
... square of the numerical measure of AD . 315. COR . III . If from a point A in the circumference of a circle chords AB and AC be drawn to the extremities of a diameter BC , and AD be drawn from A perpendicular to BC , B D AD will be a ...
... square of the numerical measure of AD . 315. COR . III . If from a point A in the circumference of a circle chords AB and AC be drawn to the extremities of a diameter BC , and AD be drawn from A perpendicular to BC , B D AD will be a ...
Side 143
... square of either side about the right angle is equal to the difference of the squares of the other two sides . * This proposition was first discovered by Pythagoras in the form given in Book IV . , Proposition XI . But the Egyptians are ...
... square of either side about the right angle is equal to the difference of the squares of the other two sides . * This proposition was first discovered by Pythagoras in the form given in Book IV . , Proposition XI . But the Egyptians are ...
Side 144
... square is equal to the side multiplied by the square root of two . и B OUTLINE PROOF : AC = √AB + BC = √2AB2 = AB√2 . PROPOSITION XVI . THEOREM 320. If through a fixed point within a circle two chords are drawn , the product of the ...
... square is equal to the side multiplied by the square root of two . и B OUTLINE PROOF : AC = √AB + BC = √2AB2 = AB√2 . PROPOSITION XVI . THEOREM 320. If through a fixed point within a circle two chords are drawn , the product of the ...
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Vanlige uttrykk og setninger
ABCD allel altitude angles are equal apothem base and altitude bisecting bisector centre chord circumference circumscribed coincide cone conical surface construct cylinder Def.-The Defs.-A diagonals diameter diedral angles distance divided draw drawn equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum given line given point given straight line GIVEN TO PROVE given triangle Hence homologous homologous sides hypotenuse intersection lateral area lateral edges lateral faces locus measured by arc middle points number of sides parallel planes parallelogram parallelopiped pass a plane perimeter PLANE GEOMETRY plane MN polyedral angle polyedron prismatic surface Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon square surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Populære avsnitt
Side 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Side 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.
Side 434 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Side 393 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 185 - To construct a square equivalent to the sum of any number of given squares.
Side 390 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Side 476 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.
Side 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.