Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 21
... extremities of the line . II . Any point without the perpendicular is un- equally distant from the extremities of the line . 12 I. Let CD be to AB at its middle point D , and P be any point on CD . To Prove P equally distant from A and ...
... extremities of the line . II . Any point without the perpendicular is un- equally distant from the extremities of the line . 12 I. Let CD be to AB at its middle point D , and P be any point on CD . To Prove P equally distant from A and ...
Seite 22
... extremities of the line . For , by 47 , all points on the perpendicular are equally distant from the extremities of the line , and all points without the perpendicular are unequally distant from the extremities of the line . Therefore ...
... extremities of the line . For , by 47 , all points on the perpendicular are equally distant from the extremities of the line , and all points without the perpendicular are unequally distant from the extremities of the line . Therefore ...
Seite 23
... extremities of another line , the first line is perpendicular to the second at its middle point . Let AB have two of its points m and n each equally distant from the extrem- ities of CD . To Prove AB 1 to CD at its middle point . Proof ...
... extremities of another line , the first line is perpendicular to the second at its middle point . Let AB have two of its points m and n each equally distant from the extrem- ities of CD . To Prove AB 1 to CD at its middle point . Proof ...
Seite 25
... extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . 56. EXERCISE . Divide a given line into quarters . Q.E.F. 57. EXERCISE . If the radius used for describing the two arcs that intersect at C in the figure of Prop . VI is ...
... extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . 56. EXERCISE . Divide a given line into quarters . Q.E.F. 57. EXERCISE . If the radius used for describing the two arcs that intersect at C in the figure of Prop . VI is ...
Seite 51
... perimeter . Suggestion . Use the preceding exercise . 176. EXERCISE . The lines AB and CD have their extremities joined by CB and AD . Prove CB + AD > AB + CD . -B PROPOSITION XXVII . THEOREM 177. If from a point within BOOK I 51 15.
... perimeter . Suggestion . Use the preceding exercise . 176. EXERCISE . The lines AB and CD have their extremities joined by CB and AD . Prove CB + AD > AB + CD . -B PROPOSITION XXVII . THEOREM 177. If from a point within BOOK I 51 15.
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Häufige Begriffe und Wortgruppen
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ
Beliebte Passagen
Seite 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Seite 163 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Seite 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Seite 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Seite 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Seite 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Seite 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Seite 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Seite 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Seite 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.