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 5
Euclides Robert Potts. XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus has all its sides equal , but its angles are not right angles . XXXIII . A rhomboid has its ...
Euclides Robert Potts. XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus has all its sides equal , but its angles are not right angles . XXXIII . A rhomboid has its ...
Side 6
... right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles ; these straight lines being continually ...
... right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side of it taken together less than two right angles ; these straight lines being continually ...
Side 14
... right angles to AB . F A D C E B In AC take any point D , and make CE equal to CD ; ( I. 3. ) upon DE describe the equilateral triangle DEF ( 1. 1 ) , and join CF. Then CF drawn from the point C , shall be at right angles to AB ...
... right angles to AB . F A D C E B In AC take any point D , and make CE equal to CD ; ( I. 3. ) upon DE describe the equilateral triangle DEF ( 1. 1 ) , and join CF. Then CF drawn from the point C , shall be at right angles to AB ...
Side 15
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with another upon one side of it , are either two right angles , or are together ...
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with another upon one side of it , are either two right angles , or are together ...
Side 16
Euclides Robert Potts. And because the angle CBE is equal to the angles CBA , ABE , add the angle EBD to each of ... right angles ; therefore the angles DBA , ABCare together equal to two right angles . ( ax . 1. ) Wherefore , when a ...
Euclides Robert Potts. And because the angle CBE is equal to the angles CBA , ABE , add the angle EBD to each of ... right angles ; therefore the angles DBA , ABCare together equal to two right angles . ( ax . 1. ) Wherefore , when a ...
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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.