Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
Results 1-5 of 32
Page 1
... vertical angle of an isosceles triangle , also bisects the base perpendicularly . Given ABC an isosceles triangle , of which the vertical angle ACB is bisected by the line CD , to prove that AB is bisected in D , and that CD is ...
... vertical angle of an isosceles triangle , also bisects the base perpendicularly . Given ABC an isosceles triangle , of which the vertical angle ACB is bisected by the line CD , to prove that AB is bisected in D , and that CD is ...
Page 3
... vertical angles at O are equal ( I. 15 ) ; consequently ( I. 4 ) the tri- angles are equal in all respects , and therefore MX = NY . M N IS Y It is evident that , in whatever direc- tion the line XY is drawn , provided it passes through ...
... vertical angles at O are equal ( I. 15 ) ; consequently ( I. 4 ) the tri- angles are equal in all respects , and therefore MX = NY . M N IS Y It is evident that , in whatever direc- tion the line XY is drawn , provided it passes through ...
Page 5
... vertical angles . Let CAB and DAB be two isosceles triangles on opposite sides of the same base AB , it is required ... angle ACD = BCD , and the angle ADC = BDC . Again , in the triangles ACE and BCE , the two sides AC and CE are equal ...
... vertical angles . Let CAB and DAB be two isosceles triangles on opposite sides of the same base AB , it is required ... angle ACD = BCD , and the angle ADC = BDC . Again , in the triangles ACE and BCE , the two sides AC and CE are equal ...
Page 6
... vertical angles at O are equal ( I. 15 ) , the alter- nate angles at M and L ( I. 29 ) are equal , and the sides KL ... angle of an isosceles triangle be a right angle , each of the angles at the base is half a right angle . Let PQR be ...
... vertical angles at O are equal ( I. 15 ) , the alter- nate angles at M and L ( I. 29 ) are equal , and the sides KL ... angle of an isosceles triangle be a right angle , each of the angles at the base is half a right angle . Let PQR be ...
Page 7
... angle CBD is greater than the angle BCD ; therefore the two angles CAD and CBD are together greater than the angle ... vertical angle , and whose bases pass through a given point , the least is that whose base is bisected in that point ...
... angle CBD is greater than the angle BCD ; therefore the two angles CAD and CBD are together greater than the angle ... vertical angle , and whose bases pass through a given point , the least is that whose base is bisected in that point ...
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 alternate angles altitude angle ACB BC² bisects the angle centre chord circumference consequently construction cut harmonically DC² describe a circle diagonals diameter dicular draw equal angles equiangular equilateral triangle Euclid 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.