The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Side
... produced . ' Dr. RUTHERFORD , Royal Military Academy , Woolwich . ' Mr. ISBISTER believes that much of the difficulty of teaching Euclid to young people arises from the absence in the ordinary edition of the Elements of those aids to ...
... produced . ' Dr. RUTHERFORD , Royal Military Academy , Woolwich . ' Mr. ISBISTER believes that much of the difficulty of teaching Euclid to young people arises from the absence in the ordinary edition of the Elements of those aids to ...
Side
... produced by the lines being scattered irregularly over the page , as in pre- vious texts of the Elements ' on this plan , the lines have been printed so as to commence uniformly from the side of the page . Every conclusion is what ...
... produced by the lines being scattered irregularly over the page , as in pre- vious texts of the Elements ' on this plan , the lines have been printed so as to commence uniformly from the side of the page . Every conclusion is what ...
Side 4
... produced ever so far both ways do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . IL . That a terminated straight line may be produced to any length in a straight ...
... produced ever so far both ways do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . IL . That a terminated straight line may be produced to any length in a straight ...
Side 5
... these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . ' PROP . I. - PROBLEM . To describe an equilateral AXIOMS . ] 5 THE SCHOOL EUCLID .
... these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . ' PROP . I. - PROBLEM . To describe an equilateral AXIOMS . ] 5 THE SCHOOL EUCLID .
Side 7
... produce the straight lines DA , DB , to E and F ; ( post . II . ) from the centre B , at the distance BC , describe the circle CGH , ( post . 3 ) and from the centre D , at the distance DG , describe the circle GKL . Then AL shall be ...
... produce the straight lines DA , DB , to E and F ; ( post . II . ) from the centre B , at the distance BC , describe the circle CGH , ( post . 3 ) and from the centre D , at the distance DG , describe the circle GKL . Then AL shall be ...
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The school Euclid: comprising the first four books, by A.K. Isbister Euclides Uten tilgangsbegrensning - 1862 |
The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Ingen forhåndsvisning tilgjengelig - 2009 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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;
Side 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,
Side 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
Side 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,
Side 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.
Side 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.
Side 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
Side 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.
Side 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
Side 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