Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Side 144
... consequent , so is the sum of all the antecedents to the sum of all the consequents . First , let there be four magnitudes , A being one antece- dent , B its consequent ; C the other antecedent , and D its consequent ; then ABA + C : B ...
... consequent , so is the sum of all the antecedents to the sum of all the consequents . First , let there be four magnitudes , A being one antece- dent , B its consequent ; C the other antecedent , and D its consequent ; then ABA + C : B ...
Side 146
... consequent as any multiple of the other antecedent is to a like multiple of its consequent ( prop . ii . ) Cor . 3. And moreover , if in any proportion like multi- ples of the first two , and also like multiples of the last two terms be ...
... consequent as any multiple of the other antecedent is to a like multiple of its consequent ( prop . ii . ) Cor . 3. And moreover , if in any proportion like multi- ples of the first two , and also like multiples of the last two terms be ...
Side 147
... consequent , so will the other antecedent be greater than , less than , or equal to its consequent . Let the proportion be A : B :: C : D. It has already been proved that if one antecedent be greater than its con- sequent , the other ...
... consequent , so will the other antecedent be greater than , less than , or equal to its consequent . Let the proportion be A : B :: C : D. It has already been proved that if one antecedent be greater than its con- sequent , the other ...
Side 148
... consequent without the multiple of the other antecedent being greater than that of its consequent , -the four magnitudes are proportional ; these multiples are also them- selves proportional ( prop.vi. ) ; and therefore by the present ...
... consequent without the multiple of the other antecedent being greater than that of its consequent , -the four magnitudes are proportional ; these multiples are also them- selves proportional ( prop.vi. ) ; and therefore by the present ...
Side 149
... consequent of the former will be greater than the consequent of the latter . In the proportion A : B :: C : D let A > C then also B > D. By inversion ( prop . viii . ) B : A :: D : C and whatever be the difference between A and C it is ...
... consequent of the former will be greater than the consequent of the latter . In the proportion A : B :: C : D let A > C then also B > D. By inversion ( prop . viii . ) B : A :: D : C and whatever be the difference between A and C it is ...
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Euclid's Elements [Book 1-6] With Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Populære avsnitt
Side 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 105 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Side 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.