Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 2
... 1. An axiom is a self - evident truth . 2. A theorem is a truth requiring demonstration . 3. A problem is a question requiring a solution . 4. A postulate is a problem the possibility of whose 2 ELEMENTS OF GEOMETRY . PLANE GEOMETRY.
... 1. An axiom is a self - evident truth . 2. A theorem is a truth requiring demonstration . 3. A problem is a question requiring a solution . 4. A postulate is a problem the possibility of whose 2 ELEMENTS OF GEOMETRY . PLANE GEOMETRY.
Página 3
... solution is self - evident . 5. A lemma is an auxiliary theorem . 6. Axioms , theorems , problems , and postulates are called propositions . 7. A corollary is an obvious consequence of one or more propositions or other premises . 8. A ...
... solution is self - evident . 5. A lemma is an auxiliary theorem . 6. Axioms , theorems , problems , and postulates are called propositions . 7. A corollary is an obvious consequence of one or more propositions or other premises . 8. A ...
Página 53
... SOLUTION . From A and B as centres , with a radius greater than one - half of AB , describe arcs intersecting at C and D. Draw the line CD : it will bisect AB in the point E. PROOF . The points C and D are equally distant from the ...
... SOLUTION . From A and B as centres , with a radius greater than one - half of AB , describe arcs intersecting at C and D. Draw the line CD : it will bisect AB in the point E. PROOF . The points C and D are equally distant from the ...
Página 54
... SOLUTION . From C as a centre , with any radius , CD , draw an arc , DE , between the sides of the angle C. From A as a centre , with the same radius , draw an indefinite arc , BF . From B as a centre , with a radius equal to the chord ...
... SOLUTION . From C as a centre , with any radius , CD , draw an arc , DE , between the sides of the angle C. From A as a centre , with the same radius , draw an indefinite arc , BF . From B as a centre , with a radius equal to the chord ...
Página 55
... SOLUTION . Through C draw any line , CD , cutting AB in D. At C , by preceding problem , construct the angle ECD equal to CDB . * Then EC is parallel to AB , since E A B D the alternate interior angles are equal ( I. , 11 ) . XXVI ...
... SOLUTION . Through C draw any line , CD , cutting AB in D. At C , by preceding problem , construct the angle ECD equal to CDB . * Then EC is parallel to AB , since E A B D the alternate interior angles are equal ( I. , 11 ) . XXVI ...
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.