Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
Results 1-5 of 19
Page 6
... double of either of the angles at the base . Let PQR ( fig . to Ex . 12 ) be an isosceles triangle , and let the side PR be produced beyond the vertex to S , then the exterior angle QRS is double of either of the angles at P or Q. For ...
... double of either of the angles at the base . Let PQR ( fig . to Ex . 12 ) be an isosceles triangle , and let the side PR be produced beyond the vertex to S , then the exterior angle QRS is double of either of the angles at P or Q. For ...
Page 8
... double of the other , prove that the hypotenuse is double of the side opposite the least angle . Let ABD be an equilateral triangle , and draw AC bisecting the angle BAD ; then BA and AC are equal to DA and AC , and the angle BAC = DAC ...
... double of the other , prove that the hypotenuse is double of the side opposite the least angle . Let ABD be an equilateral triangle , and draw AC bisecting the angle BAD ; then BA and AC are equal to DA and AC , and the angle BAC = DAC ...
Page 9
... double of D by A B G D E H hypothesis ; and taking away these equals from the preceding equal quantities , there remains angle C double of F. Or more concisely thus : but hence angle CBG = A + C , angle FEH = D + F ; CBG twice FEH by ...
... double of D by A B G D E H hypothesis ; and taking away these equals from the preceding equal quantities , there remains angle C double of F. Or more concisely thus : but hence angle CBG = A + C , angle FEH = D + F ; CBG twice FEH by ...
Page 18
... double of AOD ; and for a similar reason triangle COB is double of BOE ; but AOD = BOE , as was already proved ; hence their doubles are equal ; that is , triangle AOC F B COB ; and since these two triangles are on the same base OC ...
... double of AOD ; and for a similar reason triangle COB is double of BOE ; but AOD = BOE , as was already proved ; hence their doubles are equal ; that is , triangle AOC F B COB ; and since these two triangles are on the same base OC ...
Page 19
... double the square on BC ; whence the truth of the proposition . EXERCISE XXXIX . - THEOREM . If the two sides that contain the right angle in a right - angled triangle be 160 and 120 , prove that the hypotenuse is 200 . By proposition ...
... double the square on BC ; whence the truth of the proposition . EXERCISE XXXIX . - THEOREM . If the two sides that contain the right angle in a right - angled triangle be 160 and 120 , prove that the hypotenuse is 200 . By proposition ...
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.