The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12].1864 |
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Side 5
... parallelogram is a four - sided figure , of which the opposite sides are parallel : and the diameter , or the diagonal is the straight line joining two of its opposite angles . POSTULATES . I. LET it be granted that a straight line may ...
... parallelogram is a four - sided figure , of which the opposite sides are parallel : and the diameter , or the diagonal is the straight line joining two of its opposite angles . POSTULATES . I. LET it be granted that a straight line may ...
Side 31
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . Let ACDB be a parallelogram , of which BC is a diameter . Then the opposite sides and angles of the figure shall be equal ...
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . Let ACDB be a parallelogram , of which BC is a diameter . Then the opposite sides and angles of the figure shall be equal ...
Side 32
... parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC . Then the parallelogram ABCD shall be equal to the parallelogram EBCF . A D F A DE F A E D F WWW B B B If the sides AD , DF of the parallelograms ...
... parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC . Then the parallelogram ABCD shall be equal to the parallelogram EBCF . A D F A DE F A E D F WWW B B B If the sides AD , DF of the parallelograms ...
Side 33
... parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q. E.D. PROPOSITION XXXVII . THEOREM . Triangles ...
... parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q. E.D. PROPOSITION XXXVII . THEOREM . Triangles ...
Side 34
... parallelogram GBCA ; ( I. 34. ) also , because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of the parallelogram DEFH ; but the halves of equal things are equal ; ( ax . 7. ) therefore the ...
... parallelogram GBCA ; ( I. 34. ) also , because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of the parallelogram DEFH ; but the halves of equal things are equal ; ( ax . 7. ) therefore the ...
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Almindelige termer og sætninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære passager
Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Side 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Side 341 - On the same base, and on the same side of it, there cannot be two triangles...
Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.