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 |
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Seite vii
... common standard of reference in such an important subject , can hardly be over- estimated ; and it is extremely improbable , if Euclid were once abandoned , that any agreement would exist as to the author who should replace him . It ...
... common standard of reference in such an important subject , can hardly be over- estimated ; and it is extremely improbable , if Euclid were once abandoned , that any agreement would exist as to the author who should replace him . It ...
Seite 11
... common to the two triangles AFC , AGB ; therefore the 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 ...
... common to the two triangles AFC , AGB ; therefore the 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 ...
Seite 12
... common to both , B A LI . 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; [ Hypothesis . therefore the base DC is equal to the base AB , and ...
... common to both , B A LI . 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; [ Hypothesis . therefore the base DC is equal to the base AB , and ...
Seite 15
... common to the two triangles DAF , EAF , the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DAF is equal to the angle EAF . [ I. 8 ...
... common to the two triangles DAF , EAF , the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DAF is equal to the angle EAF . [ I. 8 ...
Seite 16
... common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DCF is equal to the angle ECF ; [ 1. 8 ...
... common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DCF is equal to the angle ECF ; [ 1. 8 ...
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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