Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα v
... re- quires a more minute examination than is suited to this place , and must , therefore , be reserved for the Notes ; but , in the mean time , it may be remarked , that no definition , except that of EUCLID , has PREFACE .
... re- quires a more minute examination than is suited to this place , and must , therefore , be reserved for the Notes ; but , in the mean time , it may be remarked , that no definition , except that of EUCLID , has PREFACE .
Σελίδα vi
... definition , except that of EUCLID , has ever been given , from which the properties of proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the ...
... definition , except that of EUCLID , has ever been given , from which the properties of proportionals can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . As to the ...
Σελίδα vii
... definitions in the first Book , and particu- larly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the ...
... definitions in the first Book , and particu- larly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the ...
Σελίδα xvi
... and that , as he has not been careful in laying the founda- tion , he will never be successful in raising the super- structure . COLLEGE OF Edinburgh , Dec. 1 , 1813 . OF GEOMETRY . BOOK I. DEFINITIONS . I. A POINT xvi PREFACE .
... and that , as he has not been careful in laying the founda- tion , he will never be successful in raising the super- structure . COLLEGE OF Edinburgh , Dec. 1 , 1813 . OF GEOMETRY . BOOK I. DEFINITIONS . I. A POINT xvi PREFACE .
Σελίδα 17
... DEFINITIONS . I. A POINT is that which has position , but not magnitude * " ( See Notes . ) A line is length without breadth . II . " COROLLARY . The extremities of a line are points ; and the inter- " sections of one line with another ...
... DEFINITIONS . I. A POINT is that which has position , but not magnitude * " ( See Notes . ) A line is length without breadth . II . " COROLLARY . The extremities of a line are points ; and the inter- " sections of one line with another ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore