Elements of Plane GeometryAmerican Book Company, 1901 - 247 σελίδες |
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Σελίδα 8
... Theorem , 22 Third proportional , 404 Transversal , 113 Transverse tangent , 556 Trapezium , 194 Trapezoid , 194 altitude of , 561 bases of , 561 Triangle , 18 altitude of , 194 equiangular , 18 equilateral , 18 isosceles , 18 median of ...
... Theorem , 22 Third proportional , 404 Transversal , 113 Transverse tangent , 556 Trapezium , 194 Trapezoid , 194 altitude of , 561 bases of , 561 Triangle , 18 altitude of , 194 equiangular , 18 equilateral , 18 isosceles , 18 median of ...
Σελίδα 12
Alan Sanders. 22. A theorem is a truth requiring demonstration . The statement of a theorem consists of two parts ... Theorems and problems are called propositions . 25. A corollary is a truth that may be readily deduced from one or more ...
Alan Sanders. 22. A theorem is a truth requiring demonstration . The statement of a theorem consists of two parts ... Theorems and problems are called propositions . 25. A corollary is a truth that may be readily deduced from one or more ...
Σελίδα 18
... theorem by this plan , the following steps are necessary : 1. The theorem is supposed to be untrue . 2. The consequences of this supposition are shown to be false . 3. Then , by the above Principle , the supposition ( that the theorem ...
... theorem by this plan , the following steps are necessary : 1. The theorem is supposed to be untrue . 2. The consequences of this supposition are shown to be false . 3. Then , by the above Principle , the supposition ( that the theorem ...
Σελίδα 19
Alan Sanders. PROPOSITION III . THEOREM 40. At a given point in a line only one perpen- dicular can be erected to that line . A B Let CD be to AB at the point D. To Prove CD is the only that can be erected to AB at D. Proof . Suppose a ...
Alan Sanders. PROPOSITION III . THEOREM 40. At a given point in a line only one perpen- dicular can be erected to that line . A B Let CD be to AB at the point D. To Prove CD is the only that can be erected to AB at D. Proof . Suppose a ...
Σελίδα 20
... C is n yards west of A , and D is n yards east of B. Prove that the distance from B to C is the same as the distance from A to D. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn 20 PLANE GEOMETRY diameter of,
... C is n yards west of A , and D is n yards east of B. Prove that the distance from B to C is the same as the distance from A to D. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn 20 PLANE GEOMETRY diameter of,
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Σελίδα 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.
Σελίδα 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.
Σελίδα 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Σελίδα 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.
Σελίδα 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.