A Text-book of Geometry

Ginn, 1888 - 386 σελίδες
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Περιεχόμενα

 STRAIGHT LINES 2 MAGNITUDE OF ANGLES 9 POSTULATES 15 THE CIRCLE 74 PROPORTIONAL LINES AND SIMILAR POLYGONS 131
 AREAS OF POLYGONS 180 22382 199 33 206 REGULAR POLYGONS AND CIRCLES 209

Δημοφιλή αποσπάσματα

Σελίδα 42 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 142 - 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 128 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 126 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Σελίδα 209 - 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 155 - 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 150 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 185 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.
Σελίδα 134 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 13 - 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.