New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 12
... straight line is the shortest line that can be drawn from one point to another . 11. All right angles are equal to ... given point parallel to another straight line . 4. That an angle may be described equal to any given angle ...
... straight line is the shortest line that can be drawn from one point to another . 11. All right angles are equal to ... given point parallel to another straight line . 4. That an angle may be described equal to any given angle ...
Page 20
... straight line , a perpen- dicular be let fall on that line , and oblique lines be drawn to different points in the same line ; 1st . The perpendicular will be shorter than any oblique line . 2d . Any two oblique lines , which meet the given ...
... straight line , a perpen- dicular be let fall on that line , and oblique lines be drawn to different points in the same line ; 1st . The perpendicular will be shorter than any oblique line . 2d . Any two oblique lines , which meet the given ...
Page 21
... straight line ; and , also , from the same point to a given straight line only two equal straight lines can be drawn . 55. Cor . 2. If a straight line have two points equally dis- tant from the extremities of another straight line , it ...
... straight line ; and , also , from the same point to a given straight line only two equal straight lines can be drawn . 55. Cor . 2. If a straight line have two points equally dis- tant from the extremities of another straight line , it ...
Page 50
... straight line which joins the center of the circle and the middle of the chord , or the middle of the arc , must be ... given points , not in the same straight line , one circumference can be made to pass , and but one . Let A , B ...
... straight line which joins the center of the circle and the middle of the chord , or the middle of the arc , must be ... given points , not in the same straight line , one circumference can be made to pass , and but one . Let A , B ...
Page 51
... given points . 149. Cor . Two circumferences can intersect in only two points ; for , if they have three points in common , they must have the same center , and must coincide . THEOREM VII . 150. A straight line perpendicular to a ...
... given points . 149. Cor . Two circumferences can intersect in only two points ; for , if they have three points in common , they must have the same center , and must coincide . THEOREM VII . 150. A straight line perpendicular to a ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - 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 through the point A a straight line parallel to BC.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.