Elementary Geometry: PlaneAmerican Book Company, 1903 - 358 σελίδες |
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Σελίδα 18
... theorem . Each step in the demonstration must be authorized by something previously accepted as true . 36. A corollary to a theorem is a statement whose truth follows at once from the truth of the theorem , or which can be proved by a ...
... theorem . Each step in the demonstration must be authorized by something previously accepted as true . 36. A corollary to a theorem is a statement whose truth follows at once from the truth of the theorem , or which can be proved by a ...
Σελίδα 19
Plane James McMahon. 39. Typical form of geometric theorem . The hypothesis of a geometric theorem can usually be put in the type - form " A is B , " and the conclusion in the form " C is D. " Each of these , considered separately , is ...
Plane James McMahon. 39. Typical form of geometric theorem . The hypothesis of a geometric theorem can usually be put in the type - form " A is B , " and the conclusion in the form " C is D. " Each of these , considered separately , is ...
Σελίδα 20
... theorem , or corollary . THEOREMS CONCERNING ANGLES 41. THEOREM 1. All straight angles are equal . Let the indefinite lines OA , OB be the sides of a straight angle whose vertex is 0 ; and let O'A ' , O'B ' be the sides of a straight ...
... theorem , or corollary . THEOREMS CONCERNING ANGLES 41. THEOREM 1. All straight angles are equal . Let the indefinite lines OA , OB be the sides of a straight angle whose vertex is 0 ; and let O'A ' , O'B ' be the sides of a straight ...
Σελίδα 21
... THEOREM 2. All right angles are equal . Let AOB , A'O'B ' be any two right angles . B B ' A To prove that these angles are equal . Ο ' A ' Every right angle is half a straight angle ( 17 , def . ) . Now all straight angles are equal ...
... THEOREM 2. All right angles are equal . Let AOB , A'O'B ' be any two right angles . B B ' A To prove that these angles are equal . Ο ' A ' Every right angle is half a straight angle ( 17 , def . ) . Now all straight angles are equal ...
Σελίδα 22
... THEOREM 4. Complements of equal angles are equal . Proof . The complement of each angle is obtained by subtracting ... THEOREM 5. The supplements of equal angles are equal . [ The proof is left to the student . ] 52. THEOREM 6. If two ...
... THEOREM 4. Complements of equal angles are equal . Proof . The complement of each angle is obtained by subtracting ... THEOREM 5. The supplements of equal angles are equal . [ The proof is left to the student . ] 52. THEOREM 6. If two ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent sides altitude angle AOB angle equal angles are equal antecedents apothem base bisector bisects called central angle central line chord circumscribed circles coincide common point construct Definition diagonal difference divided Draw drawn equal angles equal circles equiangular equilateral polygon equivalent figure given angle given circle given line given number given point given ratio greater half Hence hypotenuse included angle inscribe a regular interior angles intersect isosceles triangle less Let ABC line joining magnitudes measure-number meet the circle mid-point minor arc mth multiple n-gon number of sides number-correspondent opposite sides pair parallel parallelogram perigon perimeter perpendicular PROBLEM prolonged prove quadrangle radii radius ratio compounded rectangle regular polygon respectively equal rhombus right angle right triangle segments Show similar polygons Similarly solution statement straight angle straight line subtended surface symmetric tangent THEOREM triangle ABC unequal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 148 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Σελίδα 147 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 38 - When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other.
Σελίδα 136 - If a straight line be divided into any two parts, the square on the whole line is...
Σελίδα 195 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 80 - 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 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 263 - If four magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals, viz.
Σελίδα 307 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 287 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.