The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 sider |
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Side 8
... const . construction . By a scholium is meant a note or observation . It will be shown in the 10th proposition of the 3d book , that two circles can cut each other in only two points ; and hence there can be only two equilateral ...
... const . construction . By a scholium is meant a note or observation . It will be shown in the 10th proposition of the 3d book , that two circles can cut each other in only two points ; and hence there can be only two equilateral ...
Side 9
... ( const . ) to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal ( I. ax 1. ) to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less : which was to ...
... ( const . ) to AD ; whence AE and C are each of them equal to AD ; wherefore the straight line AE is equal ( I. ax 1. ) to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less : which was to ...
Side 12
... ( const . ) AF is equal to AG , and ( hyp . ) AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle A common to the two triangles AFC , AGB : therefore ( I. 4 . part 1. ) the base FC is ...
... ( const . ) AF is equal to AG , and ( hyp . ) AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle A common to the two triangles AFC , AGB : therefore ( I. 4 . part 1. ) the base FC is ...
Side 17
... ( const . and I. def . 17. ) to the base EF : therefore , the angle DAF is equal ( I. 8. ) to EAF ; wherefore , the given angle BAC is bisected by the line AF : which was to be done . * PROP . X. PROB . + To bisect a given finite straight ...
... ( const . and I. def . 17. ) to the base EF : therefore , the angle DAF is equal ( I. 8. ) to EAF ; wherefore , the given angle BAC is bisected by the line AF : which was to be done . * PROP . X. PROB . + To bisect a given finite straight ...
Side 18
... ( const . and I. def . 17. ) to the base EF ; therefore , the angle DCF is equal ( I. 8. ) to the angle ECF ; and they are adjacent angles . But , when the adjacent angles which one straight line makes with another straight line , are ...
... ( const . and I. def . 17. ) to the base EF ; therefore , the angle DCF is equal ( I. 8. ) to the angle ECF ; and they are adjacent angles . But , when the adjacent angles which one straight line makes with another straight line , are ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Populære avsnitt
Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 143 - 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.
Side 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Side 57 - 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 on the other part.
Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 40 - 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.
Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...