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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Página 44
... construction of Prop . 14 , Book II ; the first case of Prop . 33 , Book III , and Prop . 13 , Book vi . The definition of the segment of a circle is not once alluded to in Book 1 , and is not required before the dis- cussion of the ...
... construction of Prop . 14 , Book II ; the first case of Prop . 33 , Book III , and Prop . 13 , Book vi . The definition of the segment of a circle is not once alluded to in Book 1 , and is not required before the dis- cussion of the ...
Página 45
... construction assumed in the Elements ; and are , in fact , problems , the possibility of which is admitted to be self - evident , and to require no proof . It must , however , be carefully remarked , that the third postulate only admits ...
... construction assumed in the Elements ; and are , in fact , problems , the possibility of which is admitted to be self - evident , and to require no proof . It must , however , be carefully remarked , that the third postulate only admits ...
Página 48
... 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 given ; and the ...
... 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 given ; and the ...
Página 49
... constructions which may be admitted as possible by direct appeal to our experience ; and the axioms assert general theoretic truths so simple and self - evident as to require no proof , but to be admitted as the assumed first principles ...
... constructions which may be admitted as possible by direct appeal to our experience ; and the axioms assert general theoretic truths so simple and self - evident as to require no proof , but to be admitted as the assumed first principles ...
Página 50
... in particular terms , as it is pointed out in the diagram , and directs attention to the demonstration , by pronouncing the thing sought . 4. The construction applies the postulates to prepare the diagram 50 EUCLID'S ELEMENTS .
... in particular terms , as it is pointed out in the diagram , and directs attention to the demonstration , by pronouncing the thing sought . 4. The construction applies the postulates to prepare the diagram 50 EUCLID'S ELEMENTS .
Otras ediciones - Ver todas
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Sin vista previa disponible - 2023 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Sin vista previa disponible - 2018 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Página 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...
Página 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.
Página 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Página 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.
Página 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.
Página 341 - On the same base, and on the same side of it, there cannot be two triangles...
Página 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.