Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
Results 1-5 of 18
Page 1
... distances from the extremities of the former . Let EF be bisected perpendicularly by PL , then any point G in PL is equidistant from E and F ; and a point K , not situated in PL , is at unequal distances from E and F. For join GE , and ...
... distances from the extremities of the former . Let EF be bisected perpendicularly by PL , then any point G in PL is equidistant from E and F ; and a point K , not situated in PL , is at unequal distances from E and F. For join GE , and ...
Page 32
... distance of the foot of the perpendicular from the middle of the base is greater than or less than half the base , and it is evident that if it were equal to half the base , the triangle would be right angled . Now half the base is 2 ...
... distance of the foot of the perpendicular from the middle of the base is greater than or less than half the base , and it is evident that if it were equal to half the base , the triangle would be right angled . Now half the base is 2 ...
Page 51
... distance DE , a circle EKL be described ; it is plain that any point taken on the circum- ference will fulfil the required condition ; for the rectangle GEEF = : CE2 . COR . Since by ( III . 36 ) the rectangle GE EF = CE2 = AB2 = GF2 ...
... distance DE , a circle EKL be described ; it is plain that any point taken on the circum- ference will fulfil the required condition ; for the rectangle GEEF = : CE2 . COR . Since by ( III . 36 ) the rectangle GE EF = CE2 = AB2 = GF2 ...
Page 52
... distances of any point on the circumference from these two points is constant . Also shew that if the point taken on the circumference be on the diameter , it gives the proof of the Ninth or Tenth Propositions of the Second Book of ...
... distances of any point on the circumference from these two points is constant . Also shew that if the point taken on the circumference be on the diameter , it gives the proof of the Ninth or Tenth Propositions of the Second Book of ...
Page 58
... distance from it equal to PK , the radius of PLN . Let K be the centre of PLN , and describe a circle ( by 6th Ex . ) , KLU , passing through K , and touching UV in U ; then since OM is perpendicular to QR , it is so to UV , for angle ...
... distance from it equal to PK , the radius of PLN . Let K be the centre of PLN , and describe a circle ( by 6th Ex . ) , KLU , passing through K , and touching UV in U ; then since OM is perpendicular to QR , it is so to UV , for angle ...
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.