Elements of Geometry, Part 1Harper & Brothers, 1896 - Geometry |
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Page 5
... divided by equals , the quotients are equal ; and if unequals be divided by equals , the quotients are unequal in the same order . ( 9. ) If unequals be added to unequals , the lesser to the lesser and the greater to the greater ...
... divided by equals , the quotients are equal ; and if unequals be divided by equals , the quotients are unequal in the same order . ( 9. ) If unequals be added to unequals , the lesser to the lesser and the greater to the greater ...
Page 89
... divided by any constant k . x For is simply k ( ) x , or the product of x by a constant , which we have just proved can be made as small as we please . 189. THEOREM . The limit of the product of a constant by a variable is the product ...
... divided by any constant k . x For is simply k ( ) x , or the product of x by a constant , which we have just proved can be made as small as we please . 189. THEOREM . The limit of the product of a constant by a variable is the product ...
Page 91
... divided into any number of equal parts and apply one of these parts to A'B ' as a measure as often as it will go . Since AB and A'B ' are incommensurable , there will be a remainder XB ' less than one of these parts . Since AB and A'X ...
... divided into any number of equal parts and apply one of these parts to A'B ' as a measure as often as it will go . Since AB and A'B ' are incommensurable , there will be a remainder XB ' less than one of these parts . Since AB and A'X ...
Page 117
... divided . 269. Def . - Two straight lines are divided proportion- ally , when the ratio of one line to either of its segments is equal to the ratio of the other line to its corresponding seg . PROPOSITION I. THEOREM 270. A straight ...
... divided . 269. Def . - Two straight lines are divided proportion- ally , when the ratio of one line to either of its segments is equal to the ratio of the other line to its corresponding seg . PROPOSITION I. THEOREM 270. A straight ...
Page 119
... divided into any number of equal parts , and let one of these parts be applied to AB as a measure . Since AD and AB are incommensurable , a certain num- ber of these parts will extend from A to B ' , leaving a re- mainder BB ' less than ...
... divided into any number of equal parts , and let one of these parts be applied to AB as a measure . Since AD and AB are incommensurable , a certain num- ber of these parts will extend from A to B ' , leaving a re- mainder BB ' less than ...
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Common terms and phrases
ABCD adjacent angles altitude angles are equal angles of parallel apothem assigned quantity bisecting centre chord circumference circumscribed circle coincide decagon diagonals diameter distance divided Draw equal circles equilateral triangle Exercise exterior angle figure Find the area GEOMETRY given circle given line given point given straight line GIVEN TO PROVE given triangle GIVEN-the Hence homologous sides hypotenuse included angle intersection isosceles triangle length line parallel lines are parallel locus mean proportional measured by arc middle points number of sides opposite sides parallel axiom parallel to BC parallelogram perimeter PLANE GEOMETRY Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rectangle regular inscribed regular polygon right angles right triangle segment similar polygons straight line joining tangent THEOREM third side third straight line triangle ABC triangle whose sides triangles are equal unequal vertex vertices
Popular passages
Page 248 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 63 - To draw a straight line through a given point 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 straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Page 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Page 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 47 - ... the third side of the first is greater than the third side of the second.
Page 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.
Page 140 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.