Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Side 6
... perpendicular to each other . IX . An obtuse angle is that which is greater than a right angle . X. An acute angle is that which is less than a right angle . XI . A figure is that which is enclosed by YOUNG'S ELEMENTS OF EUCLID ,
... perpendicular to each other . IX . An obtuse angle is that which is greater than a right angle . X. An acute angle is that which is less than a right angle . XI . A figure is that which is enclosed by YOUNG'S ELEMENTS OF EUCLID ,
Side 21
... perpendicular to a given straight line of an unlimited length , from a given point with- out it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to ...
... perpendicular to a given straight line of an unlimited length , from a given point with- out it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to ...
Side 70
... perpendicular and equal to AB ; bisect * AC in E , and join B , E ; prolong CA to F , making * EF equal to EB , and from AB cut off AH equal to AF : AB shall be divided in H , so that the rectangle AB , BH is equal to the square of AH ...
... perpendicular and equal to AB ; bisect * AC in E , and join B , E ; prolong CA to F , making * EF equal to EB , and from AB cut off AH equal to AF : AB shall be divided in H , so that the rectangle AB , BH is equal to the square of AH ...
Side 71
... perpendicular be drawn from either of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the rectangle ...
... perpendicular be drawn from either of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse angle , by twice the rectangle ...
Side 72
... perpendicular let fall upon it from the opposite angle , and the acute angle . * 12 . 1 . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ...
... perpendicular let fall upon it from the opposite angle , and the acute angle . * 12 . 1 . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ...
Andre utgaver - Vis alle
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.