A Text-book of GeometryGinn, 1888 - 386 σελίδες |
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Αποτελέσματα 1 - 5 από τα 79.
Σελίδα 14
... proof or demonstration is a course of re which the truth or falsity of any statement is established . 67. A theorem is a statement to be proved . 68. A theorem consists of two parts : the hyp that which is assumed ; and the conclusion ...
... proof or demonstration is a course of re which the truth or falsity of any statement is established . 67. A theorem is a statement to be proved . 68. A theorem consists of two parts : the hyp that which is assumed ; and the conclusion ...
Σελίδα 19
... Proof . Suppose CF to be in the same line with AC . △ OCA +2 OCF = 2 rt . 4 , ( being sup . - adj . △ ) . ZOCA +2 OCB = 2 rt . 4 . § 81 § 90 Hyp . $ 55 Q.E.D. 189 :: ZOCA +2 OCF = △ OCA + ≤ OCB . Ax . 1 Take away nts of Then from ...
... Proof . Suppose CF to be in the same line with AC . △ OCA +2 OCF = 2 rt . 4 , ( being sup . - adj . △ ) . ZOCA +2 OCB = 2 rt . 4 . § 81 § 90 Hyp . $ 55 Q.E.D. 189 :: ZOCA +2 OCF = △ OCA + ≤ OCB . Ax . 1 Take away nts of Then from ...
Σελίδα 20
... Proof . LOCBL ACP . = ZOCA + 20CB = 2 rt . 4 , ( being sup . - adj . 4 ) . ZOCA + ZACP - 2 rt . s , ( being sup . - adj . 4 ) . ..LOCA +2 OCB LOCA + ZACE = Take away from each of these equals the commo Then LOCB LACP . = In like manner ...
... Proof . LOCBL ACP . = ZOCA + 20CB = 2 rt . 4 , ( being sup . - adj . 4 ) . ZOCA + ZACP - 2 rt . s , ( being sup . - adj . 4 ) . ..LOCA +2 OCB LOCA + ZACE = Take away from each of these equals the commo Then LOCB LACP . = In like manner ...
Σελίδα 22
... Proof . If AB and CD are not parallel , they sufficiently prolonged , and we shall have two pe lines from their point of meeting to the same st but this is impossible . ( From a given point without a straight line , one perpendic one ...
... Proof . If AB and CD are not parallel , they sufficiently prolonged , and we shall have two pe lines from their point of meeting to the same st but this is impossible . ( From a given point without a straight line , one perpendic one ...
Σελίδα 23
... Proof . Suppose MN drawn through CL to HK . Then But ( two lines in the same plane MN is to AB , § 100 to a given line are parallel ) . EF is to AB . Hyp . .. EF coincides with MN , § 101 ( through the same point only one line can be ...
... Proof . Suppose MN drawn through CL to HK . Then But ( two lines in the same plane MN is to AB , § 100 to a given line are parallel ) . EF is to AB . Hyp . .. EF coincides with MN , § 101 ( through the same point only one line can be ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² acute angle adjacent angles altitude angle formed angles are equal base bisector bisects called centre chord circumference circumscribed coincide construct a square decagon diagonals diameter Draw equal respectively equiangular equiangular polygon equidistant equilateral polygon equilateral triangle exterior angle feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersecting isosceles triangle legs length line drawn line joining measured by arc middle points number of sides obtuse opposite sides parallel parallelogram perimeter perpendicular PROPOSITION prove Proof quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments similar polygons square equivalent straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 46 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Σελίδα 69 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Σελίδα 187 - Two triangles having 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.
Σελίδα 64 - 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 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 215 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 161 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 135 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.