The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Σελίδα 8
... equal to C , the less . D C B A E F CONSTRUCTION From the point A draw the straight line AD equal to C ; ( 1. 2 ) ... angle BAC equal to the angle EDF . Then the base BC shall be equal to the base 8 [ BOOK I. THE SCHOOL EUCLID .
... equal to C , the less . D C B A E F CONSTRUCTION From the point A draw the straight line AD equal to C ; ( 1. 2 ) ... angle BAC equal to the angle EDF . Then the base BC shall be equal to the base 8 [ BOOK I. THE SCHOOL EUCLID .
Σελίδα 9
... angles to which the equal sides are oppo- site , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . A B C D E F DEMONSTRATION For , if the triangle ABC be applied to the triangle DEF . so ...
... angles to which the equal sides are oppo- site , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . A B C D E F DEMONSTRATION For , if the triangle ABC be applied to the triangle DEF . so ...
Σελίδα 10
... equal to one another ; and if the equal sides be produced , the angles upon the other side of the baše shall be ... angle ABC shall be equal to the angle ACв , and the angle CBD to the angle BCE . A A B C G D E In BD take any point ...
... equal to one another ; and if the equal sides be produced , the angles upon the other side of the baše shall be ... angle ABC shall be equal to the angle ACв , and the angle CBD to the angle BCE . A A B C G D E In BD take any point ...
Σελίδα 11
... equal to the remaining angles of the other , each to each , to which the equal sides are opposite , viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB ... angle ABC equal to PROP . VI . ] 11 THE SCHOOL EUCLID .
... equal to the remaining angles of the other , each to each , to which the equal sides are opposite , viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB ... angle ABC equal to PROP . VI . ] 11 THE SCHOOL EUCLID .
Σελίδα 12
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . A D B C CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the ...
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . A D B C CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the ...
Άλλες εκδόσεις - Προβολή όλων
The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles alternate angles angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre circle ABC circumference constr CONSTRUCTION cuts the circle DEMONSTRATION describe a circle describe the circle diameter double equal angles equal straight lines equal to BC equilateral and equiangular equilateral triangle Euclid exterior angle Geography given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite isosceles triangle less Let ABC Let the straight Ludgate Hill opposite angles parallel parallelogram pentagon perpendicular post 8vo produced Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment semicircle square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle دو
Δημοφιλή αποσπάσματα
Σελίδα 94 - A CONSTRUCTION For, if not let it fall otherwise, if possible, as FGDB; let F be the centre of the circle ABC, and G the centre of ADE. Join AF and AG. DEMONSTRATION Because two sides of a triangle are together greater than the third side therefore AG, GF, are greater than FA;
Σελίδα 17 - and they are adjacent angles. But, ' when a straight line standing' on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle;' (def. 10) therefore each of the angles DCF, ECF, is a right angle. Wherefore, from the point C, in the straight line AB,
Σελίδα xvii - to the same two, and when the adjacent angles are equal, they are right angles. Prop. 32. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; the angles made by this line with the line touching the circle, shall be
Σελίδα ii - at right angles to a given straight line, from a given point in the same. Prop. 13. The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Prop. 14. If, at a point in a straight line, two other straight lines,
Σελίδα 2 - XV. 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. XVL And this point is called the centre of the circle.
Σελίδα ix - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Σελίδα 118 - (i. 32) and when the adjacent angles are equal, they are right angles, (i. def. 10.) PROP. XXXII. —THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; then the angles made by this line with the line
Σελίδα iii - to four right angles. Prop. 16. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Prop. 17. Any two angles of a triangle are together less than two right angles. Prop.
Σελίδα 47 - Wherefore, triangles, &c. QED PROP. XXXVIII THEOREM. Triangles upon equal bases and between the same parallels are equal to one another. (References — Prop. i. 31, 34, 36 ; ax. 7.) Let the triangles ABC, DEF, be on the equal bases BC, EF, and between the same parallels AD, BF. Then
Σελίδα 23 - two angles of a triangle are together less than two right angles. Then any two of its angles shall be together less than two right angles, A CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC, therefore the angle ACD is greater than the interior and opposite angle