## Elements of Plane Geometry |

### From inside the book

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**Arc**is a part of the circumference ; as ,**AC**. A. Semi- circumference is an**arc**equal to half of the circumference . A Radius is a straight line extending from the centre to any point in the circumference ; as , OC . 173. A Diameter of ... Page 92

... arc . Let OC be a radius to the chord AB at D. D B C To prove that AD = BD , and

... arc . Let OC be a radius to the chord AB at D. D B C To prove that AD = BD , and

**arc AC**= arc BC . Draw the radii OA and OB . OA = OB , ( 182 ) and OD = OD ; RA AODRA BOD , ( 91 ) AD = = BD . and Also La = Lb ;**arc AC**- = arc BC . ( 186 ) ... Page 96

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**arc AC**= arc BD . Suppose the radius OE to be drawn to AB and CD . arc AE = arc BE , arc CE arc DE . Then and ( 190 ) Subtract ; then arc AE - arc CE arc BE arc DE or**arc AC**arc BD . Q. E. D. 197. SCHOLIUM . - This proposition is ... Page 101

... . ( 94 ) ( 82 ) Substitute La for its equal △ b . Then Lc 24 a . Now , ( 205 ) and c is measured by

... . ( 94 ) ( 82 ) Substitute La for its equal △ b . Then Lc 24 a . Now , ( 205 ) and c is measured by

**arc AC**; 2a is measured by**arc AC**, Za is measured by AC . CASE II . - Let the centre O fall within 9 * ELEMENTS OF PLANE GEOMETRY . 101. Page 102

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**arc AC**. Draw the diameter BD . a is measured by arc AD , and b is measured by arc DC ; ( Case I. ) . ' . a + b is measured by ( arc AD + arc DC ) , or ABC is measured by AC . CASE III . - Let the centre O fall without the inscribed ...### Other editions - View all

### Common terms and phrases

AB² ABC and DEF AC and BC acute angle adjacent angles angles are equal angles equals angles formed arc AC BC² bisectors bisects centre CF meet chord common point Concave Polygon construct Convex Polygon COR.-The decagon DEF are similar diagonal BC diameter Draw the diagonal equally distant equals two right equiangular Equilateral Polygon exterior angles given circle given straight line homologous sides hypothenuse included angle intersect La=Lb Let ABCD line joining lines drawn measured by arc medial lines middle point oblique lines parallelogram perimeter PLANE GEOMETRY produced proportion Q. E. D. THEOREM Q. E. F. PROBLEM quadrilateral radii radius rectangle regular inscribed regular polygon respectively equal rhombus right angles right-angled triangle SCHOLIUM secant similar polygons square Subtract tangent third side trapezoid triangles are equal vertex vertical angle

### Popular passages

Page 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.

Page 83 - 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 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.

Page 14 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.

Page 136 - 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, minus twice the product of one of these sides and the projection of the other side upon it.

Page 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.

Page 137 - 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 177 - 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.