Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Page 6
... produced beyond the vertex , the exterior angle is double of either of the angles at the base . Let PQR ( fig . to Ex . 12 ) be an isosceles triangle , and let the side PR be produced beyond the vertex to S , then the exterior angle QRS ...
... produced beyond the vertex , the exterior angle is double of either of the angles at the base . Let PQR ( fig . to Ex . 12 ) be an isosceles triangle , and let the side PR be produced beyond the vertex to S , then the exterior angle QRS ...
Page 7
... produced , the lines that bisect the two exterior angles , and the angle contained by the two sides produced , pass through the same point . Let ABC be a triangle , having its sides AB and AC produced to P and Q ; it is required to ...
... produced , the lines that bisect the two exterior angles , and the angle contained by the two sides produced , pass through the same point . Let ABC be a triangle , having its sides AB and AC produced to P and Q ; it is required to ...
Page 9
... Produce CA to F , and bisect the angle BAF by the line AG , and from P draw PC parallel to AG , and it is the required line . For since AG and PC are parallel , therefore ( I. 29 ) the exterior angle FAG is : = ACP , the interior and ...
... Produce CA to F , and bisect the angle BAF by the line AG , and from P draw PC parallel to AG , and it is the required line . For since AG and PC are parallel , therefore ( I. 29 ) the exterior angle FAG is : = ACP , the interior and ...
Page 10
... produce AB , DF , if necessary , to meet in G ; then the alternate angles A and AGD are equal ( I. 29 ) , because AC is parallel to DF ; and the alternate Ꭺ . angles D and AGD are also equal , since AB is parallel to DE ; consequently ...
... produce AB , DF , if necessary , to meet in G ; then the alternate angles A and AGD are equal ( I. 29 ) , because AC is parallel to DF ; and the alternate Ꭺ . angles D and AGD are also equal , since AB is parallel to DE ; consequently ...
Page 11
... produce the lines , if necessary , to meet in E ; since the angles EAC and ECA are equal , the sides EA and EC are equal , and the remaining part of the proof is the same as above . EXERCISE XXIV . - PROBLEM . Through a given point ...
... produce the lines , if necessary , to meet in E ; since the angles EAC and ECA are equal , the sides EA and EC are equal , and the remaining part of the proof is the same as above . EXERCISE XXIV . - PROBLEM . Through a given 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 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.