Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Resultat 1-5 av 52
Side 12
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to the same thing are equal to one another ; therefore CA is equal to CB : wherefore CA , AB , BC are equal to one another ...
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to the same thing are equal to one another ; therefore CA is equal to CB : wherefore CA , AB , BC are equal to one another ...
Side 14
... proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF : because , the point B coinciding with E , and C with F , if the base BC did not coincide with the base EF , two straight lines would enclose a ...
... proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF : because , the point B coinciding with E , and C with F , if the base BC did not coincide with the base EF , two straight lines would enclose a ...
Side 15
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC was proved to be equal to the angle CGB , wherefore the two triangles BFC , CGB ; are equal , and their remaining ...
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC was proved to be equal to the angle CGB , wherefore the two triangles BFC , CGB ; are equal , and their remaining ...
Side 16
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. lar . COR . - Hence every equilateral triangle is also equiangu- PROP . VI ...
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. lar . COR . - Hence every equilateral triangle is also equiangu- PROP . VI ...
Side 17
... proved to be greater than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
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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.