A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 29
... fall on opposite D B E F sides of the base . Let GBC represent the position of DEF , so that BG is the position assumed by DE , and GC the position of DF . Join AG . Then the angle BAG = BGA because BA = BG , and the angle GAC AGC ...
... fall on opposite D B E F sides of the base . Let GBC represent the position of DEF , so that BG is the position assumed by DE , and GC the position of DF . Join AG . Then the angle BAG = BGA because BA = BG , and the angle GAC AGC ...
Σελίδα 30
... fall either , 1. Within the angle BAC , as in the prop . 2. On the point A ; in which case the construction would fail ; or , 3. Outside the angle BAC ; when the line FA would have to be produced in order to bisect the angle , and the ...
... fall either , 1. Within the angle BAC , as in the prop . 2. On the point A ; in which case the construction would fail ; or , 3. Outside the angle BAC ; when the line FA would have to be produced in order to bisect the angle , and the ...
Σελίδα 44
... fall beyond it . In either case one circle would lie wholly within the other , and there would be no point of intersection . In like manner the construction would fail if A and C were not greater 44 EUCLID'S ELEMENTS .
... fall beyond it . In either case one circle would lie wholly within the other , and there would be no point of intersection . In like manner the construction would fail if A and C were not greater 44 EUCLID'S ELEMENTS .
Σελίδα 47
... fall above EF , otherwise there would be three cases to consider , viz .: 1. When G falls above EF , as in the proposition . 2. When G falls on EF , pro- duced as fig . 1. 3. When G falls below EF , as in fig . 2 . 1 2 E F The triangle ...
... fall above EF , otherwise there would be three cases to consider , viz .: 1. When G falls above EF , as in the proposition . 2. When G falls on EF , pro- duced as fig . 1. 3. When G falls below EF , as in fig . 2 . 1 2 E F The triangle ...
Σελίδα 52
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two 1 . straight lines AB , CD , make the ...
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two 1 . straight lines AB , CD , make the ...
Άλλες εκδόσεις - Προβολή όλων
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw drawn equal sides equal to AC equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Δημοφιλή αποσπάσματα
Σελίδα 90 - 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.
Σελίδα 28 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 41 - Any two sides of a triangle are together greater than the third side.
Σελίδα 57 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Σελίδα 75 - 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.
Σελίδα 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Σελίδα 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Σελίδα 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Σελίδα 69 - 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.