Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 5
... drawn between any two points . 2. A straight line may be prolonged to any length . 3. From the longer of two straight lines a part may be cut off equal to the less . 4. A straight line may be bisected ; that is , divided into two equal ...
... drawn between any two points . 2. A straight line may be prolonged to any length . 3. From the longer of two straight lines a part may be cut off equal to the less . 4. A straight line may be bisected ; that is , divided into two equal ...
Página 13
... draw AF || CD , and AG || BE . Then FAC = R , since AF || CD , and CDAC : B G E D F G A C B D E hence FAB < or > R ; but hence GABR , since AG || BE , and BE AB : GAB > or < FAB ; and the two lines , AG and AF , have not the same ...
... draw AF || CD , and AG || BE . Then FAC = R , since AF || CD , and CDAC : B G E D F G A C B D E hence FAB < or > R ; but hence GABR , since AG || BE , and BE AB : GAB > or < FAB ; and the two lines , AG and AF , have not the same ...
Página 17
... drawn through B , parallel to AC . EXERCISE 2. To what is the sum of the three exterior angles of a triangle equal ? XIX . Theorem . If , from any point within a triangle , two straight lines be drawn to the extremities of either side ...
... drawn through B , parallel to AC . EXERCISE 2. To what is the sum of the three exterior angles of a triangle equal ? XIX . Theorem . If , from any point within a triangle , two straight lines be drawn to the extremities of either side ...
Página 22
... Draw the line making DAB = DBA . line AD , Then AD = BD ( 26 ) , and AD + DC = BC ; but AD + DC > AC ( 16 ) : hence BC AC . COR . In a right - angled or an obtuse - angled triangle , the greatest side is opposite the right angle or ...
... Draw the line making DAB = DBA . line AD , Then AD = BD ( 26 ) , and AD + DC = BC ; but AD + DC > AC ( 16 ) : hence BC AC . COR . In a right - angled or an obtuse - angled triangle , the greatest side is opposite the right angle or ...
Página 23
... drawn from A to ED . PROOF . For if two perpendiculars , AB A B and AC , could be drawn , the triangle ABC would contain two right angles , ABC and ACB ; which is impossible ( 17 , 3 ) . HYPOTH . 2. ABI ED , and AC is any oblique line ...
... drawn from A to ED . PROOF . For if two perpendiculars , AB A B and AC , could be drawn , the triangle ABC would contain two right angles , ABC and ACB ; which is impossible ( 17 , 3 ) . HYPOTH . 2. ABI ED , and AC is any oblique line ...
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.