Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Side 4
... difference between two sides of a triangle is less than the third side . Let ABC be a triangle ; then the differ- ence between any two of its sides , as AB and AC , is less than the third side BC . For of the two sides AB , AC , let AB ...
... difference between two sides of a triangle is less than the third side . Let ABC be a triangle ; then the differ- ence between any two of its sides , as AB and AC , is less than the third side BC . For of the two sides AB , AC , let AB ...
Side 5
... 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 . - THEOREM . If two isosceles triangles be constructed on opposite sides of the same base ...
... 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 . - THEOREM . If two isosceles triangles be constructed on opposite sides of the same base ...
Side 11
... difference , to construct the triangle . Let BC be placed perpendicularly to AB , and join AC ; bisect AC perpendicularly by DE , and join CE ; then EBC is the required triangle . For , as in the preceding figure , the tri- = angles ADE ...
... difference , to construct the triangle . Let BC be placed perpendicularly to AB , and join AC ; bisect AC perpendicularly by DE , and join CE ; then EBC is the required triangle . For , as in the preceding figure , the tri- = angles ADE ...
Side 16
... difference of the angles at the base . Let the line CD bisect the vertical angle C of the triangle ABC , and let CE be perpendicular to its base , then the angle DCE is = half the difference of the angles at B and A ; or if the side AC ...
... difference of the angles at the base . Let the line CD bisect the vertical angle C of the triangle ABC , and let CE be perpendicular to its base , then the angle DCE is = half the difference of the angles at B and A ; or if the side AC ...
Side 20
... difference between the squares of two numbers can be found without squaring either of them , for it is always equal to the product of their sum and difference ( II . 5 Cor . ) ; thus , ( 169 +65 ) × ( 169 — 65 ) = 234 × 104 24336 as ...
... difference between the squares of two numbers can be found without squaring either of them , for it is always equal to the product of their sum and difference ( II . 5 Cor . ) ; thus , ( 169 +65 ) × ( 169 — 65 ) = 234 × 104 24336 as ...
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.