The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Side 153
... proportionals . When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second as the third is to the fourth . VII . When of the equimultiples of four magnitudes ( ( 153 ) BOOK V. ...
... proportionals . When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second as the third is to the fourth . VII . When of the equimultiples of four magnitudes ( ( 153 ) BOOK V. ...
Side 154
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continued propor- tionals , the first is said to have to the fourth the tripli- cate ratio of ...
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continued propor- tionals , the first is said to have to the fourth the tripli- cate ratio of ...
Side 155
... proportionals , so that they continue still to be proportionals : XIII . Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred , that the first is to the third as the second ...
... proportionals , so that they continue still to be proportionals : XIII . Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred , that the first is to the third as the second ...
Side 156
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which arise ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which arise ...
Side 164
... proportionals , they are proportionals also when taken inversely . If A be to B as C is to D , then also , inversely , B shall be to A as D to C. and GABE HC D F Take of B , D , any equimultiples whatever , E , F , of A , C , any ...
... proportionals , they are proportionals also when taken inversely . If A be to B as C is to D , then also , inversely , B shall be to A as D to C. and GABE HC D F Take of B , D , any equimultiples whatever , E , F , of A , C , any ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Populære avsnitt
Side 42 - 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 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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.
Side 62 - 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 of the line between the points of section, is equal to the square of half the line.
Side 22 - If from the ends of a 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.
Side 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Side 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Side 69 - 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.