The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
Im Buch
Ergebnisse 1-5 von 88
Seite 9
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which ...
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which ...
Seite 10
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
Seite 11
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , G namely the angle ACF to ...
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , G namely the angle ACF to ...
Seite 12
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the greater ; which is absurd . [ I. 4 . [ Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the greater ; which is absurd . [ I. 4 . [ Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ...
Seite 13
... base & c . Q.E.D. * PROPOSITION 8. THEOREM . 256 If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the BOOK I. 7 , 8 . 13.
... base & c . Q.E.D. * PROPOSITION 8. THEOREM . 256 If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the BOOK I. 7 , 8 . 13.
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore