Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα 35
... chord is a line joining any two points of the cir- cumference ; as , DE . 7. A segment is the part of the circle included between an arc and its chord ; as , DFE . 8. A sector is the figure included between an arc and the radii drawn to ...
... chord is a line joining any two points of the cir- cumference ; as , DE . 7. A segment is the part of the circle included between an arc and its chord ; as , DFE . 8. A sector is the figure included between an arc and the radii drawn to ...
Σελίδα 36
... chord bisects that chord . V. Theorem . Equal chords are equally distant from the centre of a circle ; and , of two unequal chords , the less is more remote from the centre . HYPOTH . 1. In the circle whose centre is O 36 [ BOOK II ...
... chord bisects that chord . V. Theorem . Equal chords are equally distant from the centre of a circle ; and , of two unequal chords , the less is more remote from the centre . HYPOTH . 1. In the circle whose centre is O 36 [ BOOK II ...
Σελίδα 37
... chords : = hence OE OF ( I. , 29 , Cor . ) . = F HYPOTH . 2. The chord CD < DA , OF 1 CD , OE L AD . TO BE PROVED . OF > OE . PROOF . Suppose the chords turned until they have the position CD and DA . Draw EF . Then , in the tri- angle ...
... chords : = hence OE OF ( I. , 29 , Cor . ) . = F HYPOTH . 2. The chord CD < DA , OF 1 CD , OE L AD . TO BE PROVED . OF > OE . PROOF . Suppose the chords turned until they have the position CD and DA . Draw EF . Then , in the tri- angle ...
Σελίδα 38
... chords . B Suppose the circles O and O ' equal . HYPOTH . 1. △ AOB = A'O'B ' . TO BE PROVED . Chord AB = A'B ' , and arc AB = A'B ' . PROOF . △ AOB ≈ A'O'B ' ( I. , 20 ) . Hence chord AB A'B ' . If the circles be applied to each ...
... chords . B Suppose the circles O and O ' equal . HYPOTH . 1. △ AOB = A'O'B ' . TO BE PROVED . Chord AB = A'B ' , and arc AB = A'B ' . PROOF . △ AOB ≈ A'O'B ' ( I. , 20 ) . Hence chord AB A'B ' . If the circles be applied to each ...
Σελίδα 39
... chord bisects the chord and its arc . VII . - DEFINITIONS . 1. The ratio of two magnitudes is the quotient obtained by dividing the numerical representative of the one by that of the other ; as , the ratio of A to B is A B 2. Two ...
... chord bisects the chord and its arc . VII . - DEFINITIONS . 1. The ratio of two magnitudes is the quotient obtained by dividing the numerical representative of the one by that of the other ; as , the ratio of A to B is A B 2. Two ...
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.