## Elements of Plane Geometry |

### From inside the book

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**common point**on the same side of a straight line equals two right angles . Thus , a +2 6+ 2 c + 4d + Le = 2 Ls . a e Α C B THEOREM III . 47. CONVERSELY . - If the sum 18 ELEMENTS OF PLANE GEOMETRY . Page 20

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**common point**equals four right angles . THEOREM V. 51. From a point without a straight line 20 ELEMENTS OF PLANE GEOMETRY . Page 21

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**point**without AB . P A D C B To prove that only one can be drawn from P to AB . Draw the oblique line PC . revolve PC so as to decrease With the**point**P fixed , a and increase b , while the**common**vertex moves in the direction CA. At ... Page 52

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**common point**. Let AE , BF , and CD be the bisectors of the As of the Δ ΑΒΓ . F C D A B To prove that AE , BF , and CD meet in a**common point**. Let AE and BF meet in a point , as O. Then is equally distant from AB and AC ; also from ... Page 53

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**common point**. In the △ ABC , let DH , FG , and EM be respectively to AC , AB , and BC , at their middle points . M C D / G E A H F B To prove that DH , FG , and EM meet at a**common point**. The Ls DH and FG meet in some point , as O ...### 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.