Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
Results 1-5 of 62
Page 1
... 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 perpendicu- lar to AB . = C For AC CB ...
... 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 perpendicu- lar to AB . = C For AC CB ...
Page 4
... triangle OBC , since the angle OBC is equal to the angle OCB , the side OB = OC ( I. 6 ) . Again , in the triangles ... ABC be a triangle ; then the differ- ence between any two of its sides , as AB and AC , is less than the third side ...
... triangle OBC , since the angle OBC is equal to the angle OCB , the side OB = OC ( I. 6 ) . Again , in the triangles ... ABC be a triangle ; then the differ- ence between any two of its sides , as AB and AC , is less than the third side ...
Page 6
... triangle be a right angle , each of the angles at the base is half a right angle . Let PQR be an isosceles triangle ... ABC be a right - angled triangle , having the right angle ACB , and let D be the middle point of the hypotenuse , to ...
... triangle be a right angle , each of the angles at the base is half a right angle . Let PQR be an isosceles triangle ... ABC be a right - angled triangle , having the right angle ACB , and let D be the middle point of the hypotenuse , to ...
Page 7
... triangle BAC is less than the triangle BDE . B E Through A draw AF parallel to BC ; then in the triangles CEP and ... ABC be a triangle , having its sides AB and AC produced to P and Q ; it is required to prove that the lines that bisect ...
... triangle BAC is less than the triangle BDE . B E Through A draw AF parallel to BC ; then in the triangles CEP and ... ABC be a triangle , having its sides AB and AC produced to P and Q ; it is required to prove that the lines that bisect ...
Page 8
... ABC is therefore a right - angled triangle , having the angle ABC double of the angle BAC , and it has been proved that BC , which is opposite the least angle , is half of BD , and B therefore half of the hypotenuse AB , which is equal ...
... ABC is therefore a right - angled triangle , having the angle ABC double of the angle BAC , and it has been proved that BC , which is opposite the least angle , is half of BD , and B therefore half of the hypotenuse AB , which is equal ...
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.