## A Text-book of Geometry |

### From inside the book

Results 1-5 of 28

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**coincide**and form one line . 7. A point is no part of a line . It is simply th the line . A point , therefore , has no dimension , b position simply . So that , if any number of poin together , they will**coincide**and form a single point ... Page 5

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**coincide**throughout their whole extent , and form but one line . 32. Two straight lines can intersect ( cut each other ) in only one point ; for if they had two points common , they would**coincide**and not intersect . 33. Of all lines ... Page 7

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**coincide**. A FIG . 7 . FIG . 8 . d α FIG . 9 . B 43. If the line AD ( Fig . 8 ) is drawn so as to divide the angle BAC into two equal parts , BAD and CAD , AD is called the bisector of the angle BAC . In general , a line that divides a ... Page 11

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**coincide**. Two angles are equal , if they can be so placed that they**coincide**. In applying this test of equality , we assume that a line may be moved from one place to another without altering its length ; that an angle may be taken up ... Page 17

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**coincide**with ED , ( because BCA and FED are straight lines and have two points common ) . Therefore the BCA is equal to the Z FED . 85. COR . 1. All right angles are equal . $ 59 86. COR . 2. The angular units , degree , minute , and ...### 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.