Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 3
... divided by equals , the quotients will be equal . 8. The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . Illustrate these axioms with the equations a = b , c = d , & c . TABLE OF SYMBOLS USED ...
... divided by equals , the quotients will be equal . 8. The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . Illustrate these axioms with the equations a = b , c = d , & c . TABLE OF SYMBOLS USED ...
Página 4
... divided by b . b a2 , a3 , . . . indicates that a is to be raised to the second , third , ✓a , · power . a , . . . indicates that the square root , cube root , .. of a is to be taken . is the sign of equality ; thus , a = b is read a ...
... divided by b . b a2 , a3 , . . . indicates that a is to be raised to the second , third , ✓a , · power . a , . . . indicates that the square root , cube root , .. of a is to be taken . is the sign of equality ; thus , a = b is read a ...
Página 5
... divided into two equal parts . II . - AXIOMS . 1. A straight line is the shortest distance between two points . 2. But one straight line can be drawn between two points . 3. Two straight lines that have two points common coin- cide ...
... divided into two equal parts . II . - AXIOMS . 1. A straight line is the shortest distance between two points . 2. But one straight line can be drawn between two points . 3. Two straight lines that have two points common coin- cide ...
Página 10
... divided into the following pairs : — -B 1 \ 2 A 5 6 78 3 D DEF . 2. Corresponding angles are an exterior and in- terior angle on the same side of the cutting line , but not ad- jacent ; as , 2 and 8 , 6 and 4 , 1 and 7 , 5 and 3 . DEF ...
... divided into the following pairs : — -B 1 \ 2 A 5 6 78 3 D DEF . 2. Corresponding angles are an exterior and in- terior angle on the same side of the cutting line , but not ad- jacent ; as , 2 and 8 , 6 and 4 , 1 and 7 , 5 and 3 . DEF ...
Página 33
... divided into four congruent triangles . 5. If the line bisecting an angle of a triangle bisects also the opposite side , it is perpendicular to that side , and the triangle is isosceles . A Prolong the bisecting line AD until DE = AD ...
... divided into four congruent triangles . 5. If the line bisecting an angle of a triangle bisects also the opposite side , it is perpendicular to that side , and the triangle is isosceles . A Prolong the bisecting line AD until DE = AD ...
Términos y frases comunes
AB² ABCD AC² adjacent angles altitude angles are equal anharmonic ratio bisect called centre chord circle circumference circumscribed polygon cone congruent construct cylinder diagonals diameter dihedrals distance divided draw equal altitudes equal bases equally distant equations equiangular EXERCISE exterior angle face angles formed frustum Geometry harmonically hence homologous HYPOTH infinite number inscribed angle intersection lateral edges line joining lines drawn locus middle point number of sides Olney's opposite sides P₁ parallel lines parallelogram parallelopiped pass perpendicular plane angle point of contact polar pole polyhedral polyhedron prism Problem PROOF proportional PROVED pyramid quadrilateral radical axis radii radius rectangle regular polygon right angles SCHOLIUM segments solid angle sphere spherical excess spherical polygon spherical triangle square straight line symmetrical tangent Theorem triangle ABC trihedrals vertex vertices
Pasajes populares
Página 19 - IF two triangles have two sides of the one equal to two sides of the...
Página 34 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Página 14 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Página 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.
Página 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.