Elements of Plane Geometry According to EuclidW. and R. Chambers, 1837 - 240 σελίδες |
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Σελίδα 110
... multiples whatsoever of the second and fourth , and if , according as the multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the ...
... multiples whatsoever of the second and fourth , and if , according as the multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the ...
Σελίδα 111
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
... multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ...
Σελίδα 113
... multiple of A + B by m ; m ( A a multiple of Á . B by m ; and m ( A + B C ) , a mul- tiple of the excess of A + B above C , by m . - Also , mA and mB are equimultiples of A and B by m . The expression m + n is the sum of the numbers m ...
... multiple of A + B by m ; m ( A a multiple of Á . B by m ; and m ( A + B C ) , a mul- tiple of the excess of A + B above C , by m . - Also , mA and mB are equimultiples of A and B by m . The expression m + n is the sum of the numbers m ...
Σελίδα 114
... multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. THEOREM . If any ...
... multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. THEOREM . If any ...
Σελίδα 115
Andrew Bell. will be the same multiple of that magnitude that the sum of the two numbers is of unity . Let AmC , and ... multiples , taken in the order of the terms , are proportional . Let A : B :: C : D , and let m and n be any two ...
Andrew Bell. will be the same multiple of that magnitude that the sum of the two numbers is of unity . Let AmC , and ... multiples , taken in the order of the terms , are proportional . Let A : B :: C : D , and let m and n be any two ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry According to Euclid Robert Simson,Formerly Chairman Department of Immunology John Playfair,John Playfair Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal angle ABC angle ACB angle BAC angle BCD angle EDF apothem base BC bisected centre chord circle ABC circumference described diameter double draw equal angles equal to AC equiangular equilateral polygon equimultiples exterior angle fore geometry given circle given line given point given rectilineal given straight line gnomon greater hypotenuse inscribed interminate less Let ABC magnitudes multiple opposite angle parallel parallelogram perimeter perpendicular polygon porism produced proportional PROPOSITION radius rectangle AB BC rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle Schol segment semicircle semiperimeter similar sine square of AC tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vulgar fraction wherefore
Δημοφιλή αποσπάσματα
Σελίδα 1 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another.
Σελίδα 73 - 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.
Σελίδα 9 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Σελίδα 4 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 139 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (2.
Σελίδα 23 - 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.
Σελίδα 129 - 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 80 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. 7. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.
Σελίδα 27 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 44 - 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.