Elements of geometry, based on Euclid, books i-iii1876 - 119 sider |
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Side 6
Edward Atkins. Thus , the angle contained by the straight lines AB and BC is ex- pressed either by ABC or CBA , and the angle contained by AB and BD is expressed either by ABD or DBA . When there is only one angle at any given point , it ...
Edward Atkins. Thus , the angle contained by the straight lines AB and BC is ex- pressed either by ABC or CBA , and the angle contained by AB and BD is expressed either by ABD or DBA . When there is only one angle at any given point , it ...
Side 10
... line whose length is the sum of the lengths of AB and BC . - expresses subtraction ; thus AB BC is the excess of the length of the line AB above that of BC . AB means the square described straight ... given finite straight line . Let AB be ...
... line whose length is the sum of the lengths of AB and BC . - expresses subtraction ; thus AB BC is the excess of the length of the line AB above that of BC . AB means the square described straight ... given finite straight line . Let AB be ...
Side 11
Edward Atkins. Proposition 2. - Problem . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line . It is required to draw from the point A a straight line ...
Edward Atkins. Proposition 2. - Problem . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line . It is required to draw from the point A a straight line ...
Side 12
... straight line AD equal to C ( I. 2 ) . From the centre A , at the distance AD , describe the circle DEF , cutting AB ... given straight lines , a part AE has been cut off , equal to C , the less . Q. E. F. * Proposition 4. - Theorem . If ...
... straight line AD equal to C ( I. 2 ) . From the centre A , at the distance AD , describe the circle DEF , cutting AB ... given straight lines , a part AE has been cut off , equal to C , the less . Q. E. F. * Proposition 4. - Theorem . If ...
Side 17
... Given DE , each to each , viz . , AB to DĒ , and AC to DF , And the base BC equal to the base EF . The angle BAC ... straight line BC on EF , The point C shall coin- cide with the point F , because BC is equal to EF ( Hyp . ) . Therefore ...
... Given DE , each to each , viz . , AB to DĒ , and AC to DF , And the base BC equal to the base EF . The angle BAC ... straight line BC on EF , The point C shall coin- cide with the point F , because BC is equal to EF ( Hyp . ) . Therefore ...
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Elements of Geometry, Based on Euclid, Bøker 1-3 Edward Atkins Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AB is equal AC and CD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle contained angle DEF angle EDF angle equal angles BGH angles CBA base BC BC is equal bisect centre circle ABC circumference diagonal diameter double draw equal circles equal to AC equal to twice EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line gnomon greater interior and opposite isosceles triangle less Let ABC Let the straight opposite angles parallel to BC parallelogram perpendicular produced PROOF PROOF.-Because Q.E.D. Proposition rectangle AD rectangle AE rectangle contained remaining angle right angle Const right angles Ax segment semicircle side BC square described square on AC touches the circle triangle ABC triangle DEF twice the rectangle
Populære avsnitt
Side 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Side 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Side 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 17 - If two triangles have two sides of the one equal to two sides of the...
Side 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Side 9 - If a straight line meet 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 71 - 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 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Side 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 69 - 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, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.