Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
From inside the book
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Page 2
... greater than GEI , and consequently in the triangle KEF the angle KFE is greater than the angle KEF , therefore ( I. 19 ) the side KE is greater than KF ; or K is unequally distant from E and F. ( 2. ) If KI were joined , the latter ...
... greater than GEI , and consequently in the triangle KEF the angle KFE is greater than the angle KEF , therefore ( I. 19 ) the side KE is greater than KF ; or K is unequally distant from E and F. ( 2. ) If KI were joined , the latter ...
Page 3
... greater than PED ; PE is greater than PD : in the same manner it can be proved that PA is greater than PE ; hence PC is the least line that can be drawn from P to the line AB , and PD is less than PE , and PE is less than PA . Also ...
... greater than PED ; PE is greater than PD : in the same manner it can be proved that PA is greater than PE ; hence PC is the least line that can be drawn from P to the line AB , and PD is less than PE , and PE is less than PA . Also ...
Page 4
... greater , and from it cut off a part , AD AC the less , then ( I. 20 ) AC and CB are A D B greater than AB or AD and DB ; and if 4 KEY TO EXPLICIT EUCLID .
... greater , and from it cut off a part , AD AC the less , then ( I. 20 ) AC and CB are A D B greater than AB or AD and DB ; and if 4 KEY TO EXPLICIT EUCLID .
Page 5
... greater than the remainder DB . When the sides AB , AC , happen to be equal , their difference is nothing , and the proposition is evident ; it is also evident when the third side BC is equal to the greater side AB . EXERCISE IX ...
... greater than the remainder DB . When the sides AB , AC , happen to be equal , their difference is nothing , and the proposition is evident ; it is also evident when the third side BC is equal to the greater side AB . EXERCISE IX ...
Page 6
... greater ; then since DC is greater than AD ( I. 18 ) , the angle CAD B is greater than the angle ACD , for a like 6 KEY TO EXPLICIT EUCLID .
... greater ; then since DC is greater than AD ( I. 18 ) , the angle CAD B is greater than the angle ACD , for a like 6 KEY TO EXPLICIT EUCLID .
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.