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 44
... Geometrical conception of an angle , which may be regarded as formed by the divergence of two straight lines from a point . In the definition of an angle , the magnitude of the angle is independent of the lengths of the two lines by ...
... Geometrical conception of an angle , which may be regarded as formed by the divergence of two straight lines from a point . In the definition of an angle , the magnitude of the angle is independent of the lengths of the two lines by ...
Side 46
... geometrical magnitudes , and the axioms , or the fundamental ideas of their equality or inequality appear to rest on the same basis . The con- ception of the truth of the axioms does not appear to be more removed from experience than ...
... geometrical magnitudes , and the axioms , or the fundamental ideas of their equality or inequality appear to rest on the same basis . The con- ception of the truth of the axioms does not appear to be more removed from experience than ...
Side 47
... Geometrical magnitudes are not admissible in Euclid's criterion of Geometrical Equality , as he has not fixed the unit of magnitude of either the straight line , the angle , or the superficies . Perhaps Euclid intended that the first ...
... Geometrical magnitudes are not admissible in Euclid's criterion of Geometrical Equality , as he has not fixed the unit of magnitude of either the straight line , the angle , or the superficies . Perhaps Euclid intended that the first ...
Side 48
... Geometrical construction is required to be effected : and it is a theorem when some Geo- metrical property is to be demonstrated . Every proposition is natu- rally divided into two parts ; a problem consists of the data , or things ...
... Geometrical construction is required to be effected : and it is a theorem when some Geo- metrical property is to be demonstrated . Every proposition is natu- rally divided into two parts ; a problem consists of the data , or things ...
Side 59
... geometrical reasoning , he may dis- pense with the aid of letters altogether , and acquire the power of express- ing in general terms the process of reasoning in the demonstration of any proposition . Also , he is advised to answer the ...
... geometrical reasoning , he may dis- pense with the aid of letters altogether , and acquire the power of express- ing in general terms the process of reasoning in the demonstration of any proposition . Also , he is advised to answer the ...
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The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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 avsnitt
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.