Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Page 6
... hypotenuse of a right - angled triangle is equally distant from each of the three angles . Let ABC be a right - angled triangle , having the right angle ACB , and let D be the middle point of the hypotenuse , to prove that AD , DC , and ...
... hypotenuse of a right - angled triangle is equally distant from each of the three angles . Let ABC be a right - angled triangle , having the right angle ACB , and let D be the middle point of the hypotenuse , to prove that AD , DC , and ...
Page 8
... hypotenuse DA is common , therefore they are equal in all respects ( I. C ) , and the angle GAD is equal to EAD , hence AD bisects the angle BAC ; and since there can only be one line drawn bisecting an angle , the lines BD , CD which ...
... hypotenuse DA is common , therefore they are equal in all respects ( I. C ) , and the angle GAD is equal to EAD , hence AD bisects the angle BAC ; and since there can only be one line drawn bisecting an angle , the lines BD , CD which ...
Page 11
... hypotenuse and a side of a right - angled triangle , and also the remaining side , to construct it . Let BC be a side of the right angle of a right - angled triangle , and AB the sum of the hypotenuse and the other side , to construct ...
... hypotenuse and a side of a right - angled triangle , and also the remaining side , to construct it . Let BC be a side of the right angle of a right - angled triangle , and AB the sum of the hypotenuse and the other side , to construct ...
Page 19
... hypotenuse is 200 . By proposition 47th , the sum of the squares on the two sides which contain the right angle is ... hypotenuse of a right - angled triangle be 169 , and one side be 65 ; prove that the other side is 156 . Since by ...
... hypotenuse is 200 . By proposition 47th , the sum of the squares on the two sides which contain the right angle is ... hypotenuse of a right - angled triangle be 169 , and one side be 65 ; prove that the other side is 156 . Since by ...
Page 20
Euclides James Pryde. Since by proposition 47th the square on the hypotenuse is equal to the sum of the squares on the two sides , the square on one side is equal to the difference between the square on the hypotenuse and the other ; but ...
Euclides James Pryde. Since by proposition 47th the square on the hypotenuse is equal to the sum of the squares on the two sides , the square on one side is equal to the difference between the square on the hypotenuse and the other ; but ...
Other editions - View all
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde No preview available - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde No preview available - 2018 |
Common terms and phrases
AB² AC² AD² altitude angle ACB BC² BD² bisects the angle centre chord circumference consequently construction cut harmonically describe a circle diagonals diameter dicular draw equal angles equiangular equilateral triangle EXERCISE exterior angle figure find a point find the locus given angle given circle given line given point greater half hence hypotenuse intersection isosceles triangle Let ABC line joining lines be drawn lines drawn opposite sides Pages parallelogram perpen perpendicular Price produced quadrilateral radius rectangle rectangle contained required locus required point required to prove required triangle right angles right-angled triangle Scholium segments semiperimeter side AC square straight line tangent touch triangle ABC Trig vertex vertical angle whence wherefore Wood-cuts
Popular passages
Page 72 - ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC.
Page 19 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 55 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 26 - Prove that three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares on the lines drawn from the vertices to the middle points of the opposite sides.
Page 73 - If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r
Page 58 - EH parallel to AB or DC, and through F draw FK parallel to AD or BC ; therefore each of the figures, AK, KB, AH, HD, AG, GC, BG...
Page 29 - The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals...
Page 24 - If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other side.
Page 2 - Of all triangles having the same vertical angle, and whose bases pass through a given point, the least is that whose base is bisected in the given point.