Essentials of GeometryS.C. Griggs, 1883 - 267 σελίδες |
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Σελίδα viii
... Definitions are introduced only as they are demanded for imme- diate use . The learner is not held for several days to the mechani- cal task of memorizing a series of abstractions , and so made to acquire at the start a distaste for the ...
... Definitions are introduced only as they are demanded for imme- diate use . The learner is not held for several days to the mechani- cal task of memorizing a series of abstractions , and so made to acquire at the start a distaste for the ...
Σελίδα 2
... DEFINITIONS . These considerations make clear the following definitions : 1. A Point is that which has position , but no extension . 2. A Line is that which has extension in one 2 PLANE GEOMETRY .
... DEFINITIONS . These considerations make clear the following definitions : 1. A Point is that which has position , but no extension . 2. A Line is that which has extension in one 2 PLANE GEOMETRY .
Σελίδα 7
... Definitions , axioms , and postulates form the basis of geometri- cal science . EXERCISES . 1. Take a square ' piece of paper , and sus- pending it in the position A B C D , move it to the position E F G H ; then the form of the entire ...
... Definitions , axioms , and postulates form the basis of geometri- cal science . EXERCISES . 1. Take a square ' piece of paper , and sus- pending it in the position A B C D , move it to the position E F G H ; then the form of the entire ...
Σελίδα 8
... definition , each of the angles ACE and ECB is a right angle ; and therefore their sum equals two right angles ; that is , ACE ECB = 2 R. Now it is plain that A CD and BCD together fill exactly the same space as ACE and E CB ; hence ...
... definition , each of the angles ACE and ECB is a right angle ; and therefore their sum equals two right angles ; that is , ACE ECB = 2 R. Now it is plain that A CD and BCD together fill exactly the same space as ACE and E CB ; hence ...
Σελίδα 9
... DEFINITIONS . If two straight lines cut , or intersect , each other , four angles are formed about the point of intersection , which are distin- guished as follows : 1. Those which lie on the same side of one of the lines and on ...
... DEFINITIONS . If two straight lines cut , or intersect , each other , four angles are formed about the point of intersection , which are distin- guished as follows : 1. Those which lie on the same side of one of the lines and on ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D ABCD adjacent angles angle equal apothem bisect central angles centre circle whose radius circumference coincide construct convex surface cylinder diagonals diameter distance divided draw drawn equal altitudes equal bases equal circles equally distant equiangular EXERCISES feet frustum generatrix given angle given circle given line given point greater Hence homologous sides hypotenuse included angle inscribed angle inscribed circle interior angles intersect isosceles triangle lune number of sides oblique parallel parallelogram parallelopiped perimeter perpendicular plane prism Prob proportional pyramid Q. E. D. Cor Q. E. F quadrilateral QUERIES radii ratio rectangle regular polygon right cone right triangle Scholium secant segments similar slant height sphere spherical triangle square straight line tangent triangle A B C vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 18 - if two triangles have two sides of the one equal to two sides of the...
Σελίδα 110 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon it.
Σελίδα 13 - If 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 two triangles will be equal.
Σελίδα 107 - 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, they are equal in all their parts.
Σελίδα 24 - 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.
Σελίδα 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Σελίδα 42 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Σελίδα 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 14 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα x - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.