A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Σελίδα 6
... circles , & c . , are all imperfect , as are also the concrete examples of these which we see around us , and all that is said of them in the definitions , or afterwards proved concerning them in the propositions , is true of these ...
... circles , & c . , are all imperfect , as are also the concrete examples of these which we see around us , and all that is said of them in the definitions , or afterwards proved concerning them in the propositions , is true of these ...
Σελίδα 8
... circles have to be described in order to cut off from a greater line a part equal to a less . The gain of such a system ... circle of strict demonstration . These postulates may be regarded as fixing the instruments which Euclid allows ...
... circles have to be described in order to cut off from a greater line a part equal to a less . The gain of such a system ... circle of strict demonstration . These postulates may be regarded as fixing the instruments which Euclid allows ...
Σελίδα 9
... a special instance selected for consideration , and the discussion is then conducted with reference to this figure . This forms the particular enunciation . Next follows the construction , directing what lines and circles INTRODUCTION . ix.
... a special instance selected for consideration , and the discussion is then conducted with reference to this figure . This forms the particular enunciation . Next follows the construction , directing what lines and circles INTRODUCTION . ix.
Σελίδα 10
Euclides Charles MANSFORD. Next follows the construction , directing what lines and circles are to be drawn to aid in the proof of the theorem or the solution of the problem . Lastly comes the demonstration , which shows by a connected ...
Euclides Charles MANSFORD. Next follows the construction , directing what lines and circles are to be drawn to aid in the proof of the theorem or the solution of the problem . Lastly comes the demonstration , which shows by a connected ...
Σελίδα 14
... circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 18. A semicircle is the figure contained by a diam- eter and the part of the circumference cut off by the ...
... circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 18. A semicircle is the figure contained by a diam- eter and the part of the circumference cut off by the ...
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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.