Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 10
... the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
... the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
Page 49
... Segments AD , is e- qual to the Rectangle com- prehended under the Seg- D B ments AD , DB , together with the Square defcribed upon the Segment AD ; that is , ABX AD × DB + AD2 . AD For raise AF perpendicular and equal to AD , and ...
... Segments AD , is e- qual to the Rectangle com- prehended under the Seg- D B ments AD , DB , together with the Square defcribed upon the Segment AD ; that is , ABX AD × DB + AD2 . AD For raise AF perpendicular and equal to AD , and ...
Page 50
... Segments AC , CB , and twice a Rect- angle comprehended under AC , CB ; that is , AD = ( AB ' ) = AC2 + CB2 + 2ACB . Upon AB make the Square AD , whofe Dia- meter is EB ; and form the Point C of Divifion , draw the Perpendicular CF to ...
... Segments AC , CB , and twice a Rect- angle comprehended under AC , CB ; that is , AD = ( AB ' ) = AC2 + CB2 + 2ACB . Upon AB make the Square AD , whofe Dia- meter is EB ; and form the Point C of Divifion , draw the Perpendicular CF to ...
Page 52
... Segments , as BC , is equal to twice the Rectangle contained under the whole Line AB ; and the faid Segment BC , together with the Square made on the other Segment AC . I fay ABCB2AB × BC + AC . De- Defcribe the Square of AB , and ...
... Segments , as BC , is equal to twice the Rectangle contained under the whole Line AB ; and the faid Segment BC , together with the Square made on the other Segment AC . I fay ABCB2AB × BC + AC . De- Defcribe the Square of AB , and ...
Page 56
... Segment GB be equal to the Square of the other Segment AG . E A F That is , ABX BG = AG2 . a Upon AB defcribe the Square AC , and bifect the Side AD in E , and draw EB , and cut off from AE continued the part EF EB , and defcribe a ...
... Segment GB be equal to the Square of the other Segment AG . E A F That is , ABX BG = AG2 . a Upon AB defcribe the Square AC , and bifect the Side AD in E , and draw EB , and cut off from AE continued the part EF EB , and defcribe a ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.