The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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... greater or less read less or greater . N.B. In the PROBLEMS , the name trapezium will be restricted to a quadrilateral , two of whose opposite sides are parallel . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . 1.
... greater or less read less or greater . N.B. In the PROBLEMS , the name trapezium will be restricted to a quadrilateral , two of whose opposite sides are parallel . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . 1.
Page 2
... greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is inclosed by one or more boundaries . xv . A circle is ...
... greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is inclosed by one or more boundaries . xv . A circle is ...
Page 5
... greater than its part . x . Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line falls upon two straight lines , so as to make the two interior angles on the same side of ...
... greater than its part . x . Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line falls upon two straight lines , so as to make the two interior angles on the same side of ...
Page 7
... greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater : it is required to ćut off from AB the greater a part equal to C the less . From the ...
... greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater : it is required to ćut off from AB the greater a part equal to C the less . From the ...
Page 8
... greater of two given straight lines , a part AE has been cut off equal to C the less . Q. E. F. PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles ...
... greater of two given straight lines , a part AE has been cut off equal to C the less . Q. E. F. PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |
Common terms and phrases
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Popular passages
Page 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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.
Page 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Page 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Page 194 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Page 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.