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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Seite 59
... shew that the intersection of two lines is a point . 5. Give Euclid's definition of a plane rectilineal angle . What are the limits of the angles considered in Geometry ? Does Euclid consider angles greater than two right angles ? 6 ...
... shew that the intersection of two lines is a point . 5. Give Euclid's definition of a plane rectilineal angle . What are the limits of the angles considered in Geometry ? Does Euclid consider angles greater than two right angles ? 6 ...
Seite 60
... side of the equilateral tri- angle DAB be produced both ways and cut the circle whose center is B and radius BC in two points G and H ; shew that either of the dis tances DG , DH may be taken as the radius 60 EUCLID'S ELEMENTS .
... side of the equilateral tri- angle DAB be produced both ways and cut the circle whose center is B and radius BC in two points G and H ; shew that either of the dis tances DG , DH may be taken as the radius 60 EUCLID'S ELEMENTS .
Seite 61
... Shew how a given straight line may be bisected by Euc . 1. 1 . 43. In what cases do the lines which bisect the interior angles of plane triangles , also bisect one , or more than one of the corresponding opposite sides of the triangles ...
... Shew how a given straight line may be bisected by Euc . 1. 1 . 43. In what cases do the lines which bisect the interior angles of plane triangles , also bisect one , or more than one of the corresponding opposite sides of the triangles ...
Seite 62
... shew that the distance between two parallel straight lines is constant ? 71. If two straight lines be not parallel , shew that all straight lines falling on them , make alternate angles , which differ by the same angle . 72. Taking as ...
... shew that the distance between two parallel straight lines is constant ? 71. If two straight lines be not parallel , shew that all straight lines falling on them , make alternate angles , which differ by the same angle . 72. Taking as ...
Seite 63
... shew that the straight line joining the vertices of the triangles is bisected by the line containing the bases . 86. If the complements ( fig . Euc . 1. 43 ) be squares , determine their relation to the whole parallelogram . 87. What is ...
... shew that the straight line joining the vertices of the triangles is bisected by the line containing the bases . 86. If the complements ( fig . Euc . 1. 43 ) be squares , determine their relation to the whole parallelogram . 87. What is ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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...
Seite 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Seite 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...
Seite 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.
Seite 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Seite 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.
Seite 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.
Seite 341 - On the same base, and on the same side of it, there cannot be two triangles...
Seite 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.