Elements of geometry, based on Euclid, books i-iii1876 - 119 σελίδες |
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Σελίδα 8
... lines are such as are in the same plane , and which being produced ever so far both ways do not meet . 35. A parallelogram is a four - sided figure of which the opposite sides are parallel ; and the diagonal is the straight line joining ...
... lines are such as are in the same plane , and which being produced ever so far both ways do not meet . 35. A parallelogram is a four - sided figure of which the opposite sides are parallel ; and the diagonal is the straight line joining ...
Σελίδα 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 line AB . Proposition 1. - Problem ...
... 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 line AB . Proposition 1. - Problem ...
Σελίδα 50
... together equal to two right angles , Therefore KH is in the same straight line with HM ( I. 14 ) . And because the straight line HG meets the parallels KM , FG , the alternate angles MHG , HGF are equal ( I. 29 ) . Add to each of these ...
... together equal to two right angles , Therefore KH is in the same straight line with HM ( I. 14 ) . And because the straight line HG meets the parallels KM , FG , the alternate angles MHG , HGF are equal ( I. 29 ) . Add to each of these ...
Σελίδα 51
... square re- quired . PROOF . - Because DE is parallel to AB , and BE parallel to AD ( Const . ) , therefore ADEB is a parallelogram ; D Therefore ... line AD meets the parallels AB , DE , the angles BAD , ADE are together equal to two right ...
... square re- quired . PROOF . - Because DE is parallel to AB , and BE parallel to AD ( Const . ) , therefore ADEB is a parallelogram ; D Therefore ... line AD meets the parallels AB , DE , the angles BAD , ADE are together equal to two right ...
Σελίδα 52
... line . BAH is a straight line . A ABD A FBC . Therefore CA is in the same straight line with AG ( I. 14 ) . For the same reason , AB and AH are in the same straight ... square Therefore the whole square BDEC is equal to the two 52 GEOMETRY .
... line . BAH is a straight line . A ABD A FBC . Therefore CA is in the same straight line with AG ( I. 14 ) . For the same reason , AB and AH are in the same straight ... square Therefore the whole square BDEC is equal to the two 52 GEOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Based on Euclid, Βιβλία 1-3 Edward Atkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 17 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.