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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Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 110
... proportion ; thus , a : b :: c : d , means that a bears the same proportion to b , as c does to d . QUESTIONS ON BOOK II . 1. Is rectangle the same as rectus angulus ? Explain the distinction , and give the corresponding Greek terms . 2 ...
... proportion ; thus , a : b :: c : d , means that a bears the same proportion to b , as c does to d . QUESTIONS ON BOOK II . 1. Is rectangle the same as rectus angulus ? Explain the distinction , and give the corresponding Greek terms . 2 ...
Σελίδα 204
... proportion , is the similitude of ratios . " IX . Proportion consists in three terms at least .
... proportion , is the similitude of ratios . " IX . Proportion consists in three terms at least .
Σελίδα 205
Euclides Robert Potts. IX . Proportion consists in three terms at least . Χ . When three magnitudes are proportionals , the first is said to have to the third , the duplicate ratio of that which it has to the second . XI . When four ...
Euclides Robert Potts. IX . Proportion consists in three terms at least . Χ . When three magnitudes are proportionals , the first is said to have to the third , the duplicate ratio of that which it has to the second . XI . When four ...
Σελίδα 206
... proportion . It is demonstrated in Prop . 22 , Book v . XX . Ex æquali in proportione perturbatâ seu inordinatâ , from equality in perturbate or disorderly proportion * . This term is used when the first magnitude is to the second of ...
... proportion . It is demonstrated in Prop . 22 , Book v . XX . Ex æquali in proportione perturbatâ seu inordinatâ , from equality in perturbate or disorderly proportion * . This term is used when the first magnitude is to the second of ...
Σελίδα 235
... Proportion is one of the most important in the whole course of mathematical truths , and it appears probable that if the subject were read simultaneously in the Algebraical and Geometrical form , the investigations of the properties ...
... Proportion is one of the most important in the whole course of mathematical truths , and it appears probable that if the subject were read simultaneously in the Algebraical and Geometrical form , the investigations of the properties ...
Άλλες εκδόσεις - Προβολή όλων
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ a₂ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC 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 AC 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 third touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Σελίδα 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...
Σελίδα 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.
Σελίδα 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 341 - On the same base, and on the same side of it, there cannot be two triangles...
Σελίδα 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.