A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Σελίδα iii
... whole body of new truths in their proper connections while no attempt is made to exhibit the relations of its several parts , or to supply applications and illustrations as the learner proceeds ; no wonder that the subject should prove ...
... whole body of new truths in their proper connections while no attempt is made to exhibit the relations of its several parts , or to supply applications and illustrations as the learner proceeds ; no wonder that the subject should prove ...
Σελίδα v
... whole subject , and form the groundwork of all the truths established in the following books . Hence it is that the definitions are placed at the very commencement , and it is important that their meaning and their proper relation to ...
... whole subject , and form the groundwork of all the truths established in the following books . Hence it is that the definitions are placed at the very commencement , and it is important that their meaning and their proper relation to ...
Σελίδα vi
... definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the groundwork of the entire subject . They supply the first principles of vi INTRODUCTION .
... definitions is the relation in which they stand to the whole system of geometry . It has been already remarked that they form the groundwork of the entire subject . They supply the first principles of vi INTRODUCTION .
Σελίδα ix
... whole of Euclid's geometrical demands , and hence are sometimes classed with the postulates ; while the first nine axioms are common notions ' which are true of all magnitudes whatever . The twelfth axiom may be more simply expressed ...
... whole of Euclid's geometrical demands , and hence are sometimes classed with the postulates ; while the first nine axioms are common notions ' which are true of all magnitudes whatever . The twelfth axiom may be more simply expressed ...
Σελίδα 18
... whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal to one another . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION ...
... whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal to one another . 12. Two straight lines which cut one another cannot both be parallel to a third straight line . PROPOSITION ...
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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
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle DBA angle EDF angle equal angles are equal axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid EUCLID'S ELEMENTS exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal
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.