## A Text-book of Geometry |

### From inside the book

Results 1-5 of 12

Page 15

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**scholium**is a remark upon some particular feature of a proposition . 77. The converse of a theorem is formed by interchanging its hypothesis and conclusion . Thus , If A is equal to B , C is equal to D. ( Direct . ) If C is equal to D ... Page 18

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**SCHOLIUM**. Adjacent angles that are supp each other are called supplementary - adjacent angle 92. COR . Since the angular magnitude about neither increased nor diminished by the number of radiate from the point , it follows that , The ... Page 19

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**SCHOLIUM**. Since Propositions II . and III . are true , their opposites are true ; namely , $ 80 If the exterior sides of two adjacent angles are not in a straight line , these angles are not supplements of each other . If two adjacent ... Page 39

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**SCHOLIUM**. In order to prove completely that a certain line is the locus of a point under a given condition , it is neces- sary to prove that every point in the line satisfies the given condition ; and secondly , that every point which ... Page 123

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**SCHOLIUM**. The intersec- tions of the bisectors of exterior angles of a triangle , formed by producing the sides of the tri- angle , are the centres of three circles , each of which will touch Q. E. F. 290. Upon a given straight line ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē 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

### Popular passages

Page 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...

Page 69 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.

Page 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.

Page 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.

Page 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 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.

Page 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.

Page 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.

Page 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 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.