The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |
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Side 15
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it ... BC is equal to BA : but it has been proved that CA finition . is equal to AB ; therefore CA , CB are each of them ...
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it ... BC is equal to BA : but it has been proved that CA finition . is equal to AB ; therefore CA , CB are each of them ...
Side 16
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line ...
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line ...
Side 17
... straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB ... BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not ...
... straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB ... BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not ...
Side 20
... straight line BC upon EF : the point C shall also coincide with the point F. Because BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
... straight line BC upon EF : the point C shall also coincide with the point F. Because BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
Side 21
... BC is equal to EF ; therefore BC coinciding with EF , BA and Book I. AC shall coincide with ED and DF ; for , if the ... straight line AF bisects the angle BAC . A b 1. 1 . Because AD is equal to AE , and AF is common to the two ...
... BC is equal to EF ; therefore BC coinciding with EF , BA and Book I. AC shall coincide with ED and DF ; for , if the ... straight line AF bisects the angle BAC . A b 1. 1 . Because AD is equal to AE , and AF is common to the two ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 28 - Any two sides of a triangle are together greater than the third side.
Side 62 - 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 28 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Side 57 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 163 - 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 17 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 189 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Side 37 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Side 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.