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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 24
... four right an- gles ; therefore all the exte- A D C B rior angles are equal to four right angles . COR . 2. The sum of the angles in a quadrilateral is equal to two right angles multiplied by 4 -2 , which amounts to four right angles ...
... four right an- gles ; therefore all the exte- A D C B rior angles are equal to four right angles . COR . 2. The sum of the angles in a quadrilateral is equal to two right angles multiplied by 4 -2 , which amounts to four right angles ...
Página 25
... four right angles ( Cor . 2 . Th . 26. ) , and the opposite angles being mutually equal , each pair of adja- cent angles must be equal to two right angles ; therefore , the opposite sides must be equal and parallel . PROP . XXVIII ...
... four right angles ( Cor . 2 . Th . 26. ) , and the opposite angles being mutually equal , each pair of adja- cent angles must be equal to two right angles ; therefore , the opposite sides must be equal and parallel . PROP . XXVIII ...
Página 33
... two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . V. PROB . To bisect a given finite 5 OF GEOMETRY . BOOK I. 33.
... two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . V. PROB . To bisect a given finite 5 OF GEOMETRY . BOOK I. 33.
Página 42
... four straight lines BA , AD , DE , EB are equal to one ano- ther , and the parallelogram ADEB is equila- D teral ; it is likewise rectangular ; for the straight line AD meeting the parallels AB , DE , makes the angles BAD , ADE equal ...
... four straight lines BA , AD , DE , EB are equal to one ano- ther , and the parallelogram ADEB is equila- D teral ; it is likewise rectangular ; for the straight line AD meeting the parallels AB , DE , makes the angles BAD , ADE equal ...
Página 44
... four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms about a diameter , to- gether with the two complements , is called a Gnomon ...
... four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms about a diameter , to- gether with the two complements , is called a Gnomon ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore