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 |
Αναζήτηση στο βιβλίο
Σελίδα v
... Proportion , the method of treating which , as it is laid down in the fifth of EUCLID , has great advantages , accompanied with considerable de- fects ; of which , however , it must be observed , that the advantages are essential , and ...
... Proportion , the method of treating which , as it is laid down in the fifth of EUCLID , has great advantages , accompanied with considerable de- fects ; of which , however , it must be observed , that the advantages are essential , and ...
Σελίδα 111
... proportion . It is demonstrated in the 22d Prop . Book 5 . XXI . Ex æquali , in proportione perturbata , seu inordinata : from equality , in perturbate , or disorderly proportion ; this term is used when the first magnitude is to the ...
... proportion . It is demonstrated in the 22d Prop . Book 5 . XXI . Ex æquali , in proportione perturbata , seu inordinata : from equality , in perturbate , or disorderly proportion ; this term is used when the first magnitude is to the ...
Σελίδα 132
... proportion- B D C als ( 4.6 . ) ; wherefore the triangles are similar ( def . 1. 6. ) . In the like manner , it may be demonstrated , that the triangle ADC is equian- : gular and similar to the triangle ABC and the 132 ELEMENTS.
... proportion- B D C als ( 4.6 . ) ; wherefore the triangles are similar ( def . 1. 6. ) . In the like manner , it may be demonstrated , that the triangle ADC is equian- : gular and similar to the triangle ABC and the 132 ELEMENTS.
Σελίδα 135
... proportion- al DB is found . Which was to be done . PROP . XIV . THEOR Equal parallelograms which have one angle of the one equa , to one angle of the other , have their sides about the equal angles reciprocally pro- portional : And ...
... proportion- al DB is found . Which was to be done . PROP . XIV . THEOR Equal parallelograms which have one angle of the one equa , to one angle of the other , have their sides about the equal angles reciprocally pro- portional : And ...
Σελίδα 136
... proportion al , viz . as DB to BE , so GB to BF ; the parallelogram AB is equal to the parallelogram BC . : Because , DB BE :: GB : BF , and DB : BE :: AB : FE , and GB : BF : BC EF , therefore , AB FE :: BC : FE ( 11. 5. ) : Wherefore ...
... proportion al , viz . as DB to BE , so GB to BF ; the parallelogram AB is equal to the parallelogram BC . : Because , DB BE :: GB : BF , and DB : BE :: AB : FE , and GB : BF : BC EF , therefore , AB FE :: BC : FE ( 11. 5. ) : Wherefore ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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