Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Side 3
... passes through the point O , the same reasoning will apply . EXERCISE V. - THEOREM . Of all lines that can be drawn from a given point to a given line , the perpendicular upon it is the least ; and of all others , that which is nearer ...
... passes through the point O , the same reasoning will apply . EXERCISE V. - THEOREM . Of all lines that can be drawn from a given point to a given line , the perpendicular upon it is the least ; and of all others , that which is nearer ...
Side 7
... pass through a given point , the least is that whose base is bisected in that point . Let ABC and DBE be two triangles having the same vertical angle DBC , and whose bases pass through the same point P , which bisects AC ; to prove that ...
... pass through a given point , the least is that whose base is bisected in that point . Let ABC and DBE be two triangles having the same vertical angle DBC , and whose bases pass through the same point P , which bisects AC ; to prove that ...
Side 8
... pass through the same point D. EXERCISE XVII . - THEOREM . If a right - angled triangle have one of the acute angles double of the other , prove that the hypotenuse is double of the side opposite the least angle . Let ABD be an ...
... pass through the same point D. EXERCISE XVII . - THEOREM . If a right - angled triangle have one of the acute angles double of the other , prove that the hypotenuse is double of the side opposite the least angle . Let ABD be an ...
Side 17
... pass through the point Q , in order that , after reflection , it might pass through P , QC would be that direction ; that is , C would be the point of incidence . Were QCP in a horizontal plane , and it were required to find the point ...
... pass through the point Q , in order that , after reflection , it might pass through P , QC would be that direction ; that is , C would be the point of incidence . Were QCP in a horizontal plane , and it were required to find the point ...
Side 25
... pass through the angular points of the former , the first parallelogram shall be equal to the sum or difference of the other two , according as they both lie without the triangle , or one of them upon it . Let ABC be a triangle , and ...
... pass through the angular points of the former , the first parallelogram shall be equal to the sum or difference of the other two , according as they both lie without the triangle , or one of them upon it . Let ABC be a triangle , and ...
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.