Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Resultat 1-5 av 23
Side 5
... and therefore A OE OF . C E F EXERCISE XI . - THEOREM . If the alternate extremities of two equal and parallel lines be joined , the connecting lines bisect each other . Let MN , KL be two equal and parallel lines FIRST BOOK . 5.
... and therefore A OE OF . C E F EXERCISE XI . - THEOREM . If the alternate extremities of two equal and parallel lines be joined , the connecting lines bisect each other . Let MN , KL be two equal and parallel lines FIRST BOOK . 5.
Side 6
... alternate extremities , bisect each other in O. For in the two triangles MON , KOL , the vertical angles at O are equal ( I. 15 ) , the alter- nate angles at M and L ( I. 29 ) are equal , and the sides KL , MN are also equal ; therefore ...
... alternate extremities , bisect each other in O. For in the two triangles MON , KOL , the vertical angles at O are equal ( I. 15 ) , the alter- nate angles at M and L ( I. 29 ) are equal , and the sides KL , MN are also equal ; therefore ...
Side 9
... FAG is : = ACP , the interior and opposite ; and GAB is = ABC , as they are alternate angles ; but FAG GAB by construction , consequently F ACP ABC . - G P B A C When the point lies between the given lines , or FIRST BOOK . 9.
... FAG is : = ACP , the interior and opposite ; and GAB is = ABC , as they are alternate angles ; but FAG GAB by construction , consequently F ACP ABC . - G P B A C When the point lies between the given lines , or FIRST BOOK . 9.
Side 10
... 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 angles A and D being each = AGD are equal . F G B D E ...
... 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 angles A and D being each = AGD are equal . F G B D E ...
Side 13
... alternate angles GAP and PBE are equal , and PBE = DAP ( I. 5 ) ; hence GAP = DAP , and the angles at G and D of the triangles APG , APD are right angles , and the side AP is common ; hence the triangles are equal ( I. 26 ) , and ...
... alternate angles GAP and PBE are equal , and PBE = DAP ( I. 5 ) ; hence GAP = DAP , and the angles at G and D of the triangles APG , APD are right angles , and the side AP is common ; hence the triangles are equal ( I. 26 ) , 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.