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 8
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
Página 10
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . And , since it ...
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . And , since it ...
Página 12
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same ...
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same ...
Página 13
... Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . 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 ...
... Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . 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 ...
Página 14
... Wherefore from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Q.E.F. COR . By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be ...
... Wherefore from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Q.E.F. COR . By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be ...
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.