A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página v
... axioms , which , with the accompanying defi- nitions , underlie the 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 ...
... axioms , which , with the accompanying defi- nitions , underlie the 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 ...
Página viii
... AXIOMS . From the elementary properties of geome- trical figures stated in the definitions we may at once proceed to ... axioms , and these with the corresponding definitions form the basis of all our reasonings respect- ing them . Like ...
... AXIOMS . From the elementary properties of geome- trical figures stated in the definitions we may at once proceed to ... axioms , and these with the corresponding definitions form the basis of all our reasonings respect- ing them . Like ...
Página ix
... axiom may be more simply expressed thus , " Two straight lines which cut one another cannot be both parallel to a third straight line . ” 6 The definitions and axioms together include all the fundamental principles from which the truths ...
... axiom may be more simply expressed thus , " Two straight lines which cut one another cannot be both parallel to a third straight line . ” 6 The definitions and axioms together include all the fundamental principles from which the truths ...
Página x
... axioms so as to obtain new truths . These results are then used to establish further and more complex truths , and so the process is continued until all the truths which constitute the science of geometry are demonstrated , and their ...
... axioms so as to obtain new truths . These results are then used to establish further and more complex truths , and so the process is continued until all the truths which constitute the science of geometry are demonstrated , and their ...
Página xi
... axioms ( ' Ax : ' ) , constructions ( ' Const : ' ) , & c . , show whence the statements to which they are attached have been derived . Thus starting with the elementary truths in the definitions and axioms Euclid proceeds to prove ...
... axioms ( ' Ax : ' ) , constructions ( ' Const : ' ) , & c . , show whence the statements to which they are attached have been derived . Thus starting with the elementary truths in the definitions and axioms Euclid proceeds to prove ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 28 - If two triangles have two sides of the one equal to two sides of the...
Página 41 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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...
Página 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.
Página 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.