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 22
... line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the ... BC is equal to AB : But it has been proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now ...
... line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the ... BC is equal to AB : But it has been proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now ...
Σελίδα 23
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line ...
... BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line ...
Σελίδα 24
... line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with ... BC shall coincide with the base EF ( cor . def 3 , ) , and shall be equal to it . Therefore also the whole triangle ...
... line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with ... BC shall coincide with the base EF ( cor . def 3 , ) , and shall be equal to it . Therefore also the whole triangle ...
Σελίδα 27
... line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but ...
... line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but ...
Σελίδα 28
... line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal ...
... line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal ...
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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