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 xv
... construction then usually follows , which states the necessary straight lines and circles which must be drawn in ... construction is required ; and sometimes the construction and demonstration are com- bined . The demonstration is a ...
... construction then usually follows , which states the necessary straight lines and circles which must be drawn in ... construction is required ; and sometimes the construction and demonstration are com- bined . The demonstration is a ...
Seite xvi
... construction that has been made , or which are given in the supposition of the proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning ...
... construction that has been made , or which are given in the supposition of the proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning ...
Seite 9
... Construction . Therefore AE and Care each of them equal to AD . Therefore AE is equal to C. [ Axiom 1 . Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 ...
... Construction . Therefore AE and Care each of them equal to AD . Therefore AE is equal to C. [ Axiom 1 . Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 ...
Seite 15
... Construction . and AF is 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 ...
... Construction . and AF is 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 ...
Seite 16
... Construction . and CF is 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 ...
... Construction . and CF is 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 ...
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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