Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 12
... respectively paral- lel , and lying both in the same or both in opposite directions , they are eml HYPOTH . BA || ED , and BC || Theorem . If two pa 1. The corresponding EF . 2. The alternate angle 3. The sum of two angles . HYPOTH . AB ...
... respectively paral- lel , and lying both in the same or both in opposite directions , they are eml HYPOTH . BA || ED , and BC || Theorem . If two pa 1. The corresponding EF . 2. The alternate angle 3. The sum of two angles . HYPOTH . AB ...
Σελίδα 13
... respectively par- allel to them , have not the same direction , and will meet if sufficiently produced . EXERCISE 1. Prove this by an auxiliary line , BC . EXERCISE 2. The lines bisecting two adjacent angles are perpendicular to each ...
... respectively par- allel to them , have not the same direction , and will meet if sufficiently produced . EXERCISE 1. Prove this by an auxiliary line , BC . EXERCISE 2. The lines bisecting two adjacent angles are perpendicular to each ...
Σελίδα 14
... respectively taken in the same order are equal each to each . DEF . 6. Two polygons are congruent when they are both mutually equilateral and equiangular . It is evident that they may be applied to each other so as to correspond in all ...
... respectively taken in the same order are equal each to each . DEF . 6. Two polygons are congruent when they are both mutually equilateral and equiangular . It is evident that they may be applied to each other so as to correspond in all ...
Σελίδα 16
... respectively equal to two angles of another triangle , the third angles are also equal , and the triangles are mutually equiangular . COR . 3. Every triangle must have at least two acute angles ; for , if two were obtuse or right angles ...
... respectively equal to two angles of another triangle , the third angles are also equal , and the triangles are mutually equiangular . COR . 3. Every triangle must have at least two acute angles ; for , if two were obtuse or right angles ...
Σελίδα 41
... respectively divided into 7 and 4 angles , which are equal , since they belong to equal arcs ( 6 ) . Hence and ZAOB = 7 ZAOC 4 ' ZAOB arc AB ZAOC = arc AC Let AC be di- 2. Suppose the arcs incommensurable . vided into n equal parts ...
... respectively divided into 7 and 4 angles , which are equal , since they belong to equal arcs ( 6 ) . Hence and ZAOB = 7 ZAOC 4 ' ZAOB arc AB ZAOC = arc AC Let AC be di- 2. Suppose the arcs incommensurable . vided into n equal parts ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.