Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 19
... contained by the sides of that which has the greater third side will be greater than the angle contained by the sides of the other . HYPOTH . AB = DE , AC DF , BC > EF . TO BE PROVED . BAC > EDF . PROOF . If BAC is not > EDF , да either ...
... contained by the sides of that which has the greater third side will be greater than the angle contained by the sides of the other . HYPOTH . AB = DE , AC DF , BC > EF . TO BE PROVED . BAC > EDF . PROOF . If BAC is not > EDF , да either ...
Página 23
... contain two right angles , ABC and ACB ; which is impossible ( 17 , 3 ) . HYPOTH . 2. ABI ED , and AC is any oblique line . TO BE PROVED . AB < AC . PROOF . In the triangle ABC , hence HYPOTH . 3. BC ACB < ABC = R ( 17 , 3 ) : ABAC ( 28 ) ...
... contain two right angles , ABC and ACB ; which is impossible ( 17 , 3 ) . HYPOTH . 2. ABI ED , and AC is any oblique line . TO BE PROVED . AB < AC . PROOF . In the triangle ABC , hence HYPOTH . 3. BC ACB < ABC = R ( 17 , 3 ) : ABAC ( 28 ) ...
Página 39
... contained an exact number of times in each . This third magnitude is called the common measure . When two magnitudes ... contain exactly m of those parts , their ratio will be m n 3. If , however , the second magnitude contains m Воок ІІ ...
... contained an exact number of times in each . This third magnitude is called the common measure . When two magnitudes ... contain exactly m of those parts , their ratio will be m n 3. If , however , the second magnitude contains m Воок ІІ ...
Página 40
... contains m of those parts , with a remainder less than the common measure , the m fraction will be an approximate ... contained in another quantity . VIII . Theorem . Incommensurable ratios are equal , if their ap- proximate ratios ...
... contains m of those parts , with a remainder less than the common measure , the m fraction will be an approximate ... contained in another quantity . VIII . Theorem . Incommensurable ratios are equal , if their ap- proximate ratios ...
Página 41
... contain it 4 times . Then arc AB = 7 arc AC 4 Draw radii to the points of division . For ex- B The centre angles AOB ... contains m of those parts , with a remainder less than one of the parts . To the points of division draw radii ...
... contain it 4 times . Then arc AB = 7 arc AC 4 Draw radii to the points of division . For ex- B The centre angles AOB ... contains m of those parts , with a remainder less than one of the parts . To the points of division draw radii ...
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.