Plane and Solid GeometryGinn, 1913 - 470 sider |
Inni boken
Resultat 1-5 av 44
Side v
... PROPORTIONAL LINES SIMILAR POLYGONS NUMERICAL PROPERTIES OF FIGURES PROBLEMS OF CONSTRUCTION EXERCISES PAGE 1 25 26 46 51 59 68 73 77 84 85 93 93 94 96 102 109 112 126 • 140 141 151 151 157 165 174 182 187 PAGE BOOK IV . AREAS OF ...
... PROPORTIONAL LINES SIMILAR POLYGONS NUMERICAL PROPERTIES OF FIGURES PROBLEMS OF CONSTRUCTION EXERCISES PAGE 1 25 26 46 51 59 68 73 77 84 85 93 93 94 96 102 109 112 126 • 140 141 151 151 157 165 174 182 187 PAGE BOOK IV . AREAS OF ...
Side 151
... Proportional . The fourth term of a proportion is called the fourth proportional to the terms taken in order . Thus in the proportion a : bc : d , d is the fourth proportional to a , b , and c . ... H .. are 260. Continued Proportion ...
... Proportional . The fourth term of a proportion is called the fourth proportional to the terms taken in order . Thus in the proportion a : bc : d , d is the fourth proportional to a , b , and c . ... H .. are 260. Continued Proportion ...
Side 152
... proportional between two quantities is equal to the square root of their product . For if a : bb : c , then b2 = ac ( § 261 ) , and b = √ac , by Ax . 5 . 263. COROLLARY 2. If the two antecedents of a proportion are equal , the two ...
... proportional between two quantities is equal to the square root of their product . For if a : bb : c , then b2 = ac ( § 261 ) , and b = √ac , by Ax . 5 . 263. COROLLARY 2. If the two antecedents of a proportion are equal , the two ...
Side 157
... proportionally . M B Given the triangle ABC , with EF drawn parallel to BC . To prove that EB : AE = FC : AF . CASE 1. When AE and EB are commensurable . Proof . Assume that MB is a common ... PROPORTIONAL LINES 157 PROPORTIONAL LINES.
... proportionally . M B Given the triangle ABC , with EF drawn parallel to BC . To prove that EB : AE = FC : AF . CASE 1. When AE and EB are commensurable . Proof . Assume that MB is a common ... PROPORTIONAL LINES 157 PROPORTIONAL LINES.
Side 159
... proportional intercepts on any two transversals . Then AL Now and Draw AN II to CD . A C $ 127 FL G HM K § 273 CG , LM = GK , MN = KD . AH : AM AF : AL = FH : LM , § 274 = AH : AM = HB : MN . : . AF : CG = FH ; GK = HB : KD . Ax . 9 B N ...
... proportional intercepts on any two transversals . Then AL Now and Draw AN II to CD . A C $ 127 FL G HM K § 273 CG , LM = GK , MN = KD . AH : AM AF : AL = FH : LM , § 274 = AH : AM = HB : MN . : . AF : CG = FH ; GK = HB : KD . Ax . 9 B N ...
Andre utgaver - Vis alle
Vanlige uttrykk og setninger
AABC ABCD altitude angles are equal apothem bisector bisects called chord circular cone circumference circumscribed coincide cone of revolution congruent conic surface construct COROLLARY cube diagonal diameter dihedral angles distance draw equidistant equilateral triangle equivalent EXERCISE face angles figure Find the area Find the locus Find the volume frustum given circle given line given point greater hypotenuse inscribed intersection isosceles triangle lateral area lateral edges lateral faces lune measured by arc mid-point number of sides oblique parallel lines parallelogram perimeter perpendicular plane geometry plane MN polyhedral angle polyhedron Proof proportional prove quadrilateral radii radius ratio rectangle rectangular parallelepiped regular polygon regular pyramid right angle right prism right section right triangle segments slant height sphere spherical polygon spherical triangle square straight angle straight line surface symmetric tangent tetrahedron THEOREM triangle ABC trihedral vertex vertices
Populære avsnitt
Side 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Side 360 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Side 190 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Side 152 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Side 54 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Side 31 - In an isosceles triangle the angles opposite the equal sides are equal.
Side 77 - 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. Given A ABC and A'B'C...
Side 51 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 22 - The following are the most important axioms used in geometry: 1. If equals are added to equals the sums are equal. 2. If equals are subtracted from equals the remainders are equal. 3. If equals are multiplied by equals the products are equal. 4. If equals are divided by equals the quotients are equal.
Side 213 - The square constructed upon the sum of two lines is equivalent to the sum of the squares constructed upon these two lines, increased by twice the rectangle of these lines.