A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página v
... axioms , which , with the accompanying definitions , 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 , and ...
... axioms , which , with the accompanying definitions , 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 , and ...
Página viii
... AXIOMS . From the elementary properties of geometrical 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 respecting them . Like the ...
... AXIOMS . From the elementary properties of geometrical 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 respecting them . Like the ...
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 . " 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 . " 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 ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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 EDF angle equal angles are equal angles CBA axioms base BC BC is equal bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid 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 PROPOSITION 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