Euclid's Elements of geometry, books i. ii. iii. iv1862 |
Inni boken
Resultat 1-5 av 74
Side 7
... 1. ) Conclusion . - Therefore , from AB , the greater of two given straight lines , a part AE has been cut off ... Demonstration . - 1 . For if the triangle ABC be applied to ( or placed upon ) the triangle DEF , 2. So that the point A ...
... 1. ) Conclusion . - Therefore , from AB , the greater of two given straight lines , a part AE has been cut off ... Demonstration . - 1 . For if the triangle ABC be applied to ( or placed upon ) the triangle DEF , 2. So that the point A ...
Side 8
... 1 . In BD take any point F. 2. From AE , the greater , cut off AG , equal to AF , the less . ( I. 3. ) 3. Join FC , GB . D F B A E Demonstration . - 1 . Because AF is equal to AG . ( constr . ) And AB is equal to AC . ( hypoth ...
... 1 . In BD take any point F. 2. From AE , the greater , cut off AG , equal to AF , the less . ( I. 3. ) 3. Join FC , GB . D F B A E Demonstration . - 1 . Because AF is equal to AG . ( constr . ) And AB is equal to AC . ( hypoth ...
Side 9
... one of them is greater than the other . Let AB be the greater . Construction . - 1 . From AB the greater , cut off a part DB , equal to AC the less . ( I. 3. ) 2. Join DC . Demonstration . - 1 . Because in the triangles DBC BOOK I. PROP . 6 ...
... one of them is greater than the other . Let AB be the greater . Construction . - 1 . From AB the greater , cut off a part DB , equal to AC the less . ( I. 3. ) 2. Join DC . Demonstration . - 1 . Because in the triangles DBC BOOK I. PROP . 6 ...
Side 10
Euclides. Demonstration . - 1 . Because in the triangles DBC , ACB , DB is assumed to be equal to AC , and BC is common to both , 2. Therefore the two sides DB , BC , are equal to the two sides AC , CB , each to each . 3. And the angle ...
Euclides. Demonstration . - 1 . Because in the triangles DBC , ACB , DB is assumed to be equal to AC , and BC is common to both , 2. Therefore the two sides DB , BC , are equal to the two sides AC , CB , each to each . 3. And the angle ...
Side 11
... one of the triangles fall within the other . Construction . - Produce AC , AD , to E and F , and join CD . Demonstration . - 1 . Because AC is assumed to be equal to AD . ( hyp . ) 2. The triangle ADC is an isosceles triangle , and the ...
... one of the triangles fall within the other . Construction . - Produce AC , AD , to E and F , and join CD . Demonstration . - 1 . Because AC is assumed to be equal to AD . ( hyp . ) 2. The triangle ADC is an isosceles triangle , and the ...
Vanlige uttrykk og setninger
AB is equal AC and CB adjacent angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal bisected circle ABC circumference Conclusion Conclusion.-Therefore const Construction.-1 Demonstration.-1 describe the circle diameter double equal angles equal to CD equiangular exterior angle given circle given point given rectilineal angle given straight line Given.-Let ABCD gnomon greater Hypothesis inscribed interior and opposite isosceles triangle less opposite angle parallel to CD parallelogram perpendicular point F produced Q. E. D. PROPOSITION rectangle AB BC rectangle AE rectangle contained rectilineal figure References-Prop remaining angle required to describe right angles segment semicircle Sequence side BC square on AC straight line AC straight line drawn touches the circle triangle ABC triangle DEF twice the rectangle
Populære avsnitt
Side 25 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.
Side 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 99 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Side 66 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Side 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 58 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.