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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Page 6
... less than two right angles ; these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral ...
... less than two right angles ; these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral ...
Page 8
... less . Let AB and C be the two given straight lines , of which AB is the greater . It is required to cut off from AB the greater , a part equal to C , the less . D E B F From the point A draw the straight line AD equal to C ; ( 1. 2 ...
... less . Let AB and C be the two given straight lines , of which AB is the greater . It is required to cut off from AB the greater , a part equal to C , the less . D E B F From the point A draw the straight line AD equal to C ; ( 1. 2 ...
Page 18
... less than two right angles . Let ABC be any triangle . Then any two of its angles together shall be less than two right angles . A B C D Produce any side BC to D. Then because ACD is the exterior angle of the triangle ABC ; therefore ...
... less than two right angles . Let ABC be any triangle . Then any two of its angles together shall be less than two right angles . A B C D Produce any side BC to D. Then because ACD is the exterior angle of the triangle ABC ; therefore ...
Page 19
... less than AB , then the angle ABC would be less than the angle ACB ; ( 1. 18. ) but it is not less , ( hyp . ) therefore the side AC is not less than AB ; and AC has been shewn to be not equal to AB ; therefore AC is greater than AB ...
... less than AB , then the angle ABC would be less than the angle ACB ; ( 1. 18. ) but it is not less , ( hyp . ) therefore the side AC is not less than AB ; and AC has been shewn to be not equal to AB ; therefore AC is greater than AB ...
Page 20
... less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD , CD be drawn to a point D within the ...
... less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from the points B , C , the ends of the side BC , let the two straight lines BD , CD be drawn to a point D within the ...
Other editions - View all
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides No preview available - 2023 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides No preview available - 2018 |
The School Edition. Euclid's Elements of Geometry, the First Six Books, by R ... Euclides No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Page 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...
Page 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.
Page 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Page 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.
Page 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.
Page 341 - On the same base, and on the same side of it, there cannot be two triangles...
Page 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.