The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
Im Buch
Ergebnisse 1-5 von 96
Seite 13
... which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . Book I. 2 X. Two straight lines cannot enclose a OF EUCLID . 13 POSTULATES. ...
... which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . Book I. 2 X. Two straight lines cannot enclose a OF EUCLID . 13 POSTULATES. ...
Seite 17
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
Seite 18
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; the remainder BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each ...
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; the remainder BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each ...
Seite 37
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal to two ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal to two ...
Seite 39
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another ; also , their diameter bisects them ...
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another ; also , their diameter bisects them ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore