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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Page 36
... whole , or the remainder AE , is equal to the whole , or the re- mainder DF : And AB is equal to DC ; therefore the two EA , AB are equal to the two FD , DC , each to A D P A DE FAED F W W C B B с each , and the angle EAB is equal to ...
... whole , or the remainder AE , is equal to the whole , or the re- mainder DF : And AB is equal to DC ; therefore the two EA , AB are equal to the two FD , DC , each to A D P A DE FAED F W W C B B с each , and the angle EAB is equal to ...
Page 41
... whole figure ABCD , and are therefore called the complements : the comple- ment BK is equal to the complement KD . For because ABCD is a parallelogram , and AC its E A H B G D K F diameter , E 3 BOOK I. 41 gram that shall be equal to ...
... whole figure ABCD , and are therefore called the complements : the comple- ment BK is equal to the complement KD . For because ABCD is a parallelogram , and AC its E A H B G D K F diameter , E 3 BOOK I. 41 gram that shall be equal to ...
Page 42
... whole triangle ABC is equal to the whole triangle ADC ; therefore the remainder , the complement BK , is equal to the remainder , the complement KD . Wherefore , The complements & c . Q. E.D. PROP . XLIV . PROB . To a given straight ...
... whole triangle ABC is equal to the whole triangle ADC ; therefore the remainder , the complement BK , is equal to the remainder , the complement KD . Wherefore , The complements & c . Q. E.D. PROP . XLIV . PROB . To a given straight ...
Page 44
... whole parallelogram FKML is equal to the whole rectilineal figure ABCD : Wherefore the parallelogram FKML has been described equal to the given rectilineal figure ABCD , and having the angle FKM equal to the given angle E. Q. E. F. COR ...
... whole parallelogram FKML is equal to the whole rectilineal figure ABCD : Wherefore the parallelogram FKML has been described equal to the given rectilineal figure ABCD , and having the angle FKM equal to the given angle E. Q. E. F. COR ...
Page 46
... whole angle DBA is equal to the whole FBC : And because the two sides AB , BD are equal to the two FB , BC , each to each , and the angle DBA is equal to the angle FBC - therefore the base AD is equal to the base FC , and the triangle ...
... whole angle DBA is equal to the whole FBC : And because the two sides AB , BD are equal to the two FB , BC , each to each , and the angle DBA is equal to the angle FBC - therefore the base AD is equal to the base FC , and the triangle ...
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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.