Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Side 41
... touch one another , either internally or externally , the chords of the two arcs , intercepted between two lines drawn through the point of contact , are parallel . A E Let ACO , BDO be two circles touching in O ; and AB , CD any two ...
... touch one another , either internally or externally , the chords of the two arcs , intercepted between two lines drawn through the point of contact , are parallel . A E Let ACO , BDO be two circles touching in O ; and AB , CD any two ...
Side 42
... touching a given circle . Let A , B be the given points , and CDT the given circle , to describe a circle through A and B , to touch CDT . Let any circle passing through A and B cut the given circle in C and D ; draw CD and AB , and ...
... touching a given circle . Let A , B be the given points , and CDT the given circle , to describe a circle through A and B , to touch CDT . Let any circle passing through A and B cut the given circle in C and D ; draw CD and AB , and ...
Side 43
... touch in T ; for the tangent lies be- tween them , so that they can meet only in the point T ( III . 11 and 12 ) . Α . T B P If a circle be described through A , B , and T ' , it could be similarly proved that it would touch the given ...
... touch in T ; for the tangent lies be- tween them , so that they can meet only in the point T ( III . 11 and 12 ) . Α . T B P If a circle be described through A , B , and T ' , it could be similarly proved that it would touch the given ...
Side 47
... touch a given circle in a given point , and also touch a given straight line . Let ABC be the given circle of which D is the centre , A the given point , and EF the given straight line ; THIRD BOOK . 47.
... touch a given circle in a given point , and also touch a given straight line . Let ABC be the given circle of which D is the centre , A the given point , and EF the given straight line ; THIRD BOOK . 47.
Side 48
... touch the given circle in A , and also touch the given straight line EF . From A draw AG a tangent . to the circle ABC ( III . 17 ) , and produce it to meet EF in G ; bisect the angle AGF by the straight line GH , and produce DA to meet ...
... touch the given circle in A , and also touch the given straight line EF . From A draw AG a tangent . to the circle ABC ( III . 17 ) , and produce it to meet EF in G ; bisect the angle AGF by the straight line GH , and produce DA to meet ...
Andre utgaver - Vis alle
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... Euclides Uten tilgangsbegrensning - 1860 |
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 72 - ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC.
Side 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.
Side 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.
Side 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.
Side 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
Side 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...
Side 29 - The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals...
Side 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.
Side 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.