The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 7
... shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the ...
... shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the ...
Σελίδα 22
... shown , that the angle CEB is equal to the anglẹ AED . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the point where they ...
... shown , that the angle CEB is equal to the anglẹ AED . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the point where they ...
Σελίδα 26
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore , in any triangle , & c . Q. E. D. PROP . XX.- THEOREM . Any two sides of a triangle are together greater than the third side . ( References - Prop . 1. 3 ...
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore , in any triangle , & c . Q. E. D. PROP . XX.- THEOREM . Any two sides of a triangle are together greater than the third side . ( References - Prop . 1. 3 ...
Σελίδα 28
... shown that BA , AC , are greater than BE , EC , much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( 1. 16 ) therefore the exterior ...
... shown that BA , AC , are greater than BE , EC , much more then are BA , AC , greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( 1. 16 ) therefore the exterior ...
Σελίδα 34
... shown to be equal to EF , the two AB , BC , are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; ( hyp . ) therefore the base AC is equal to the base DF , and the third angle BAC to the third angle ...
... shown to be equal to EF , the two AB , BC , are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; ( hyp . ) therefore the base AC is equal to the base DF , and the third angle BAC to the third angle ...
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 constr CONSTRUCTION cuts the circle DEMONSTRATION describe a circle describe the circle diameter double equal angles equal straight lines equal to BC equiangular pentagon 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 References-Prop remaining angle right angles segment semicircle side BC square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle
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