Elements of Plane Geometry: For the Use of Schools |
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Page 13
... similar manner it may be shown that CEB - AED . PROP . IV . THEOREM . If two sides and the included angle , in one triangle , be respectively equal to the two sides and included an- gle in another triangle , these two triangles will be ...
... similar manner it may be shown that CEB - AED . PROP . IV . THEOREM . If two sides and the included angle , in one triangle , be respectively equal to the two sides and included an- gle in another triangle , these two triangles will be ...
Page 16
... similar manner it may be proved that BC cannot be longer than AC ; therefore they must be equal . Cor . Every equiangular triangle is equilateral . PROP . VIII . THEOREM . Two angles are equal when they have their sides par- allel and ...
... similar manner it may be proved that BC cannot be longer than AC ; therefore they must be equal . Cor . Every equiangular triangle is equilateral . PROP . VIII . THEOREM . Two angles are equal when they have their sides par- allel and ...
Page 21
... larger than C ; and ABC , which exceeds ABD , must be still larger than C. In a similar manner , if the side AC is taken longer than BC , may we prove the angle ABC to be larger than A. 22 SUM OF TWO SIDES OF TRIANGLES . [ BOOK 21 ...
... larger than C ; and ABC , which exceeds ABD , must be still larger than C. In a similar manner , if the side AC is taken longer than BC , may we prove the angle ABC to be larger than A. 22 SUM OF TWO SIDES OF TRIANGLES . [ BOOK 21 ...
Page 48
... similar , and the longest side , as above , must be opposite the given angle ( B. I. Prop . 15 ) . We will now consider the second of the above cases , In this case , if the side where the given angle is acute . opposite the given angle ...
... similar , and the longest side , as above , must be opposite the given angle ( B. I. Prop . 15 ) . We will now consider the second of the above cases , In this case , if the side where the given angle is acute . opposite the given angle ...
Page 55
... - bers , the products of the corresponding terms will be pro- portional . If and then will 2 : 3 :: 6 : 9 , 4:87 : 14 , 8 : 24 : 42 : 126 . LA BOOK V. DEFINITIONS . 1. Similar figures are those ,. BOOK IV . ] 55 PROPORTIONS .
... - bers , the products of the corresponding terms will be pro- portional . If and then will 2 : 3 :: 6 : 9 , 4:87 : 14 , 8 : 24 : 42 : 126 . LA BOOK V. DEFINITIONS . 1. Similar figures are those ,. BOOK IV . ] 55 PROPORTIONS .
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Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast No preview available - 2013 |
Common terms and phrases
ABCD adjacent angles allel alternate angles altitude angle ABC angles ABD angles is equal antecedent and consequent B. I. Ax base centre circle whose radius circumference circumscribed circumscribed circle Converse of Prop describe an arc diagonal diameter divide draw the line equal angles equal B. I. Prop equal chords equal Prop equal respectively equiangular equivalent feet given angle given line given point given side half hence the triangles hypotenuse included angle inscribed angle Let the triangles line drawn linear units longer than AC multiplied number of sides oblique lines parallel to CD parallelogram perimeter perpendicular PROBLEM prove radii rectangle regular polygons respectively equal right angles Prop right-angled triangle Scholium sides AC similar subtended tangent THEOREM three sides triangles ABC triangles are equal vertex
Popular passages
Page 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 70 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 53 - In any proportion, the product of the means is equal to the product of the extremes.
Page 87 - 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.
Page 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 81 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Page 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.