The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Σελίδα 102
... proportional between the other two . t 10. When there is any number of magnitudes of the same kind , greater than two , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of ...
... proportional between the other two . t 10. When there is any number of magnitudes of the same kind , greater than two , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of ...
Σελίδα 108
... proportional ; then , if the first be greater than the second , the third is also greater than the fourth ; and , if equal , equal ; if less , less . Take any like multiples of each of them , as the doubles of each ; then ( V. def . 5 ...
... proportional ; then , if the first be greater than the second , the third is also greater than the fourth ; and , if equal , equal ; if less , less . Take any like multiples of each of them , as the doubles of each ; then ( V. def . 5 ...
Σελίδα 128
... proportional , and if the first be divided by the second , and the third by the fourth , the quotients are equal . A C Let AB :: C : D ; then = B D If A and B be whole numbers , let the first and third terms be multiplied by B , and the ...
... proportional , and if the first be divided by the second , and the third by the fourth , the quotients are equal . A C Let AB :: C : D ; then = B D If A and B be whole numbers , let the first and third terms be multiplied by B , and the ...
Σελίδα 129
... proportional numbers be made the numerator and denominator of one fraction , and the third and fourth those of another , the two fractions are equal . This is the same in substance as that the two expressions , A : B :: C : D , A C and ...
... proportional numbers be made the numerator and denominator of one fraction , and the third and fourth those of another , the two fractions are equal . This is the same in substance as that the two expressions , A : B :: C : D , A C and ...
Σελίδα 131
... proportional , the sum of the first and second terms is to their difference , as the sum of the third and fourth terms is to their difference . It is evident that if B be greater than A , the analogy will become B + A : B — A :: D + Č ...
... proportional , the sum of the first and second terms is to their difference , as the sum of the third and fourth terms is to their difference . It is evident that if B be greater than A , the analogy will become B + A : B — A :: D + Č ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - 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.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - 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 on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 32 - 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.
Σελίδα 40 - 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.
Σελίδα 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...