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 262
... suppose the angles at C and F obtuse angles . The demonstration is similar to the above . Lastly , suppose one of the angles a right angle , namely , the angle C. If the angle B be not equal to the angle E , make the E B A B angle ABG ...
... suppose the angles at C and F obtuse angles . The demonstration is similar to the above . Lastly , suppose one of the angles a right angle , namely , the angle C. If the angle B be not equal to the angle E , make the E B A B angle ABG ...
Seite 268
... suppose we have a square , and let its side be 5 inches in length . Then , by our rule , the area of the square is 5 times 5 square inches , that is 25 square inches . Now the number 25 is called in Arithmetic the square of the number 5 ...
... suppose we have a square , and let its side be 5 inches in length . Then , by our rule , the area of the square is 5 times 5 square inches , that is 25 square inches . Now the number 25 is called in Arithmetic the square of the number 5 ...
Seite 270
... suppose AC not perpendicular to BC . CB , BD , together with the square on CD . To each of these equals add the square on DA . [ II . 7 . Therefore the squares on CB , BD , DA are equal to twice the rectangle CB , BD , together with the ...
... suppose AC not perpendicular to BC . CB , BD , together with the square on CD . To each of these equals add the square on DA . [ II . 7 . Therefore the squares on CB , BD , DA are equal to twice the rectangle CB , BD , together with the ...
Seite 271
... suppose AC perpendicular to BC . Then BC is the straight line intercepted be- tween the perpendicular and the acute angle at B. And the square on AB is equal to the squares on AC , CB . [ I. 47 . Therefore the square on AC is less than ...
... suppose AC perpendicular to BC . Then BC is the straight line intercepted be- tween the perpendicular and the acute angle at B. And the square on AB is equal to the squares on AC , CB . [ I. 47 . Therefore the square on AC is less than ...
Seite 275
... Suppose that A is double of B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as- sumed that the difference of A and C is double 18-2 ...
... Suppose that A is double of B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as- sumed that the difference of A and C is double 18-2 ...
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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