Elements of Geometry and Conic Sections |
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Page 25
... perpen- dicular to AB through its middle point , C. F E First . Every point of EF is equally dis- tant from the extremities of the line AB ; for , since AC is equal to CB , the two oblique lines AD , DB are equally distant from the A ...
... perpen- dicular to AB through its middle point , C. F E First . Every point of EF is equally dis- tant from the extremities of the line AB ; for , since AC is equal to CB , the two oblique lines AD , DB are equally distant from the A ...
Page 27
... perpen- dicular to BD . For the sum of the angles ABD and ABF is equal to two right angles ( Prop . II . ) ; and by hypothesis the sum of the angles ABD and BAC is equal to two right an- gles . Therefore , the sum of ABD and ABF is ...
... perpen- dicular to BD . For the sum of the angles ABD and ABF is equal to two right angles ( Prop . II . ) ; and by hypothesis the sum of the angles ABD and BAC is equal to two right an- gles . Therefore , the sum of ABD and ABF is ...
Page 57
... perpen- dicular let fall from the vertex of an angle on the opposite side , taken as a base , or on the base produced . 7. The altitude of a parallelogram is the perpendicular drawn BOOK IV . 57 The Proportions of Figures BOOK IV.
... perpen- dicular let fall from the vertex of an angle on the opposite side , taken as a base , or on the base produced . 7. The altitude of a parallelogram is the perpendicular drawn BOOK IV . 57 The Proportions of Figures BOOK IV.
Page 67
... perpen- dicular to BC produced ; the square of AC is greater than the squares of AB , BC by twice the rectangle BCX BD . For CD is equal to BC + BD ; therefore CD ' A = BC ' + BD ' + 2BC × BD ( Prop . VIII . ) . To each of these equals ...
... perpen- dicular to BC produced ; the square of AC is greater than the squares of AB , BC by twice the rectangle BCX BD . For CD is equal to BC + BD ; therefore CD ' A = BC ' + BD ' + 2BC × BD ( Prop . VIII . ) . To each of these equals ...
Page 83
... perpen- dicular , raised from the middle point of AB ( Prop . XVIII . Cor . , B. I. ) . Therefore the line DE divides the line AB into two equal parts at the point C. PROBLEM II . To draw a perpendicular to a straight BOOK V. 83 BOOK V ...
... perpen- dicular , raised from the middle point of AB ( Prop . XVIII . Cor . , B. I. ) . Therefore the line DE divides the line AB into two equal parts at the point C. PROBLEM II . To draw a perpendicular to a straight BOOK V. 83 BOOK V ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project No preview available - 2016 |
Common terms and phrases
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Page 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Page 63 - 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.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 17 - 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.
Page 148 - I.), that every section of a sphere made by a plane is a circle.