The Elements of Plane and Solid GeometryLongmans, Green, and Company, 1872 - 285 sider |
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Resultat 1-5 av 35
Side 68
... divided , at the given point are equal to each other respectively . 4. A chord , DC , is drawn in a circle and produced to A , so that CA is equal to the radius of the circle . If the diameter AEB be drawn , prove that the angle DEB is ...
... divided , at the given point are equal to each other respectively . 4. A chord , DC , is drawn in a circle and produced to A , so that CA is equal to the radius of the circle . If the diameter AEB be drawn , prove that the angle DEB is ...
Side 114
... may be of equal length . 9. Given two concentric circles , draw a straight line which shall be divided into three equal parts in its points of inter- section with the two circles . 115 BOOK IV . ON AREAS . SECTION I. - 114 Geometry .
... may be of equal length . 9. Given two concentric circles , draw a straight line which shall be divided into three equal parts in its points of inter- section with the two circles . 115 BOOK IV . ON AREAS . SECTION I. - 114 Geometry .
Side 115
... divided into the same number of parts , such that to every part of one of the figures there is a corresponding part of the second figure which can be superposed , as in case 1 , upon the corresponding part of the first figure . Fig . 1 ...
... divided into the same number of parts , such that to every part of one of the figures there is a corresponding part of the second figure which can be superposed , as in case 1 , upon the corresponding part of the first figure . Fig . 1 ...
Side 117
... divided by either diagonal are equal to each other in area , and therefore that the area of the parallelogram is double of the area of either of these triangles . PROPOSITION 2 . Two parallelograms which have two adjacent sides and the ...
... divided by either diagonal are equal to each other in area , and therefore that the area of the parallelogram is double of the area of either of these triangles . PROPOSITION 2 . Two parallelograms which have two adjacent sides and the ...
Side 125
... the parallelogram . PROPOSITION II . If there be two straight lines , one of which is divided into any number of parts , the rectangle of the two straight li shall be equal to the sum of the rectangles of Book IV . - Theorems . 125.
... the parallelogram . PROPOSITION II . If there be two straight lines , one of which is divided into any number of parts , the rectangle of the two straight li shall be equal to the sum of the rectangles of Book IV . - Theorems . 125.
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ABC and DEF ABCD AC is equal adjacent angles angle ABC angle BAC antecedent area of AC bisects the angle centre chords circumference coincide common measure containing Corollary 2.-If DEFINITION diameter dicular dihedral angle distance divided equal angles equal in area equal to AB equal to AC exterior angle finite straight line given angle given circle given plane given point given ratio given straight line greater homologous incommensurable inscribed length less Let ABC line joining locus middle point multiple number of sides numerator and denominator opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 14 proved radius ratio be equal rectangle regular polygon respectively equal right angles segments Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Populære avsnitt
Side 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Side 285 - Price 31. 6d. On the STRENGTH of MATERIALS and STRUCTURES : the Strength of Materials as depending on their quality and as ascertained by Testing Apparatus ; the Strength of Structures, as depending on their form and arrangement, and on the materials of which they are composed. By Sir J.
Side 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 285 - Fcp. 8vo. , 41. 6d. INTRODUCTION TO THE STUDY OF INORGANIC CHEMISTRY. By WILLIAM ALLEN MILLER, MD, LL.D., FRS With 72 Illustrations.
Side 19 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other.
Side 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Side 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 285 - THEORY OF HEAT. By J. CLERK MAXWELL. MA, LL.D., Edin., FRSS., L. & E. With 38 Illustrations. Fcp. 8vo. , 41. 6d. PRACTICAL PHYSICS. By RT GLAZEBROOK. MA, FRS, and W. N. SHAW, MA * With 134 Illustrations. Fcp. 8vo. , 71. 6d. PRELIMINARY SURVEY AND ESTIMATES. By THEODORE GRAHAM GRIBBLE, Civil Engineer.
Side 204 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 30 - Any two angles of a triangle are together less than two right angles.