Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 5
... Circumference , and dividing the Circle in- to two equal Parts . 18. A Semi - circle is a Figure which is con- tained under the Diameter , and under that part of the Circumference which is cut off by the Diameter . In the Circle EABCD ...
... Circumference , and dividing the Circle in- to two equal Parts . 18. A Semi - circle is a Figure which is con- tained under the Diameter , and under that part of the Circumference which is cut off by the Diameter . In the Circle EABCD ...
Página 13
... Circumference thereof . Then is AGCB . g conft . For DG DE , and DA DC . Where- 3 ax . fore AGCE BC AG . Which was k 14x . i is def to be done . = g The Pofition of the Point A within or with- out the Line BC varies the Cafes , but the ...
... Circumference thereof . Then is AGCB . g conft . For DG DE , and DA DC . Where- 3 ax . fore AGCE BC AG . Which was k 14x . i is def to be done . = g The Pofition of the Point A within or with- out the Line BC varies the Cafes , but the ...
Página 44
... Circumference in E , and draw BE . Then fhalla BE ( BA ' ) = BC ' + CE ' . Whence " BA ' -BC - CE ' . QE . F с 47. 1 . B 47. I. PROB . C A 2 III . Any two Sides of a right- angled Triangle ABC being given ; to find the third Side . Let ...
... Circumference in E , and draw BE . Then fhalla BE ( BA ' ) = BC ' + CE ' . Whence " BA ' -BC - CE ' . QE . F с 47. 1 . B 47. I. PROB . C A 2 III . Any two Sides of a right- angled Triangle ABC being given ; to find the third Side . Let ...
Página 59
... Circumference in H. Then fhall CH ML = A. с For draw GH ; then is A " = DB = * DCF = HC ML . Q. E.D. - GF GC 2 C.45 . I. d conft . e 5.2 . & ax 3 . 47. 1. & Зах . End of the Second Book . ( 60 ) EUCLID's ELEMENTS . E BOOK III . Book II ...
... Circumference in H. Then fhall CH ML = A. с For draw GH ; then is A " = DB = * DCF = HC ML . Q. E.D. - GF GC 2 C.45 . I. d conft . e 5.2 . & ax 3 . 47. 1. & Зах . End of the Second Book . ( 60 ) EUCLID's ELEMENTS . E BOOK III . Book II ...
Página 62
... Circumference of the Circle ( ADC ) : then the Ang . ABC is faid to Stand upon that Circumference . A B 9. A Sector of a Circle ( ACB ) . is a Figure comprehended under the right Lines AC , BC drawn from the Center C , and the Cir ...
... Circumference of the Circle ( ADC ) : then the Ang . ABC is faid to Stand upon that Circumference . A B 9. A Sector of a Circle ( ACB ) . is a Figure comprehended under the right Lines AC , BC drawn from the Center C , and the Cir ...
Términos y frases comunes
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe BC Baſe becauſe bifect Center Circ Cone confequently conft COROL Cylinder defcribed demonftrated Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples EUCLID's ELEMENTS faid fame Multiple fecond fhall fimilar fince firft folid fome fore four right ftanding given right Line gles Gnomon greater Hence infcribe leffer lefs likewife Line CD Magnitudes manifeft manner Number oppofite Paral parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular poffible Point Polyhedron Prifms Probl PROP Propofition Pyramids Ratio Rectangle right Angles right Line AB right Line AC right-lined Figure SCHOL SCHOLIU Segment ſhall Side BC Sphere Square thefe thofe thro tiple Triangle ABC Whence whofe whole
Pasajes populares
Página 31 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 145 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Página 33 - ABD, is equal* to two right angles, «13. 1. therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are sides of the figure; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles; therefore all the exterior angles are equal to four right angles.
Página 27 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Página 31 - The three angles of any triangle taken together are equal to the three angles of any other triangle taken together. From whence it follows, 2.
Página 11 - That a straight line may be drawn from any point to any other point. 2. That a straight line may be produced to any length in a straight line.