## Elements of Euclid Adapted to Modern Methods in Geometry |

### From inside the book

Results 1-5 of 37

Page 13

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**circumference**; and is such that all straight lines drawn from a certain point within it to the**circumference**are equal to one another . This point is called the centre of the circle . 31. An arc of a circle is any part of the ... Page 16

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**circumference**shall pass through the other . But this restriction has been abandoned by most geometers , and the compasses used to carry distances . In this way many problems are greatly simplified , complicated constructions being ... Page 32

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**circumference**of the circle RN , must be outside the circle RM . Again , DR and RO are ( hyp . ) greater than DO , and if the equal radii OR and OH be taken from both , the remainder DR is greater than the remainder DH ( ax . 5 ) ; that ... Page 33

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**circumference**of RN is within the circle RM ( Def . 34 , cor . ) . But N is without it . Since then the point H is within the circle RM , and N without it , the circles must intersect . Cor . - Hence at a given point P , in a given line ... Page 64

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**circumference**. Such numbers are called in- commensurable . Hence it is that , in applying arithmetic and algebra to the solution of geometrical problems , we meet with difficulties which have no place in the methods followed by Euclid ...### Other editions - View all

Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) No preview available - 1874 |

### Common terms and phrases

AC and CB altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference cloth coincide Const conv Cor.-Hence diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle Fcap GEOGRAPHY geometrical given circle given line given point given straight line greater half the perimeter Hence hypotenuse inscribed intersecting isosceles triangle less Let ABC LL.D meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure reflex angle remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent THEOREM triangle ABC twice the rectangle twice the square whole line

### Popular passages

Page 68 - 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.

Page 77 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.

Page 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.

Page 30 - Any two sides of a triangle are together greater than the third side.

Page 204 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...

Page 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.