Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 5
... fall from a certain Point within the Figure , are equal to one another . 16. And that Point is called the Center of the Circle . -B E A C D 17. A Diameter of a Circle is a right Line drawn through the Center thereof , terminating both ...
... fall from a certain Point within the Figure , are equal to one another . 16. And that Point is called the Center of the Circle . -B E A C D 17. A Diameter of a Circle is a right Line drawn through the Center thereof , terminating both ...
Página 11
... falling on two right Lines AD , CB , makes the internal Angles on B I A D the fame Side B AD + ABC lefs than two right Angles : thofe two right Lines produced , fhall meet on that Side , where the Angles are lefs than two right Angles ...
... falling on two right Lines AD , CB , makes the internal Angles on B I A D the fame Side B AD + ABC lefs than two right Angles : thofe two right Lines produced , fhall meet on that Side , where the Angles are lefs than two right Angles ...
Página 15
... fall upon B , because ab AB alfo the right Line ac fhall fall up- on AC , because the Angle Aa ; moreover , a hyp . the Point ofhall fall upon the Point C , because AC ac . Therefore the right Lines bc , BC , because they have the fame ...
... fall upon B , because ab AB alfo the right Line ac fhall fall up- on AC , because the Angle Aa ; moreover , a hyp . the Point ofhall fall upon the Point C , because AC ac . Therefore the right Lines bc , BC , because they have the fame ...
Página 17
... falls in AC , it is manifeft that AD is not equal to AC . Cafe 2. If the Point D falls within the Tri- angle ACB , then draw the Line CD , and con- tinue out BDF and BCE . Now if you fay that AD AC , then will the Angle ADC b beb 5. 1 ...
... falls in AC , it is manifeft that AD is not equal to AC . Cafe 2. If the Point D falls within the Tri- angle ACB , then draw the Line CD , and con- tinue out BDF and BCE . Now if you fay that AD AC , then will the Angle ADC b beb 5. 1 ...
Página 18
... fall on a , ( for it cannot fall on any other Point , by the laft Propofition ; ) and fo the Sides of the An- gles A and a do coincided : wherefore those Angles are equal . Q. E. D. COROLLARIES . 1. Hence Triangles mutually equilateral ...
... fall on a , ( for it cannot fall on any other Point , by the laft Propofition ; ) and fo the Sides of the An- gles A and a do coincided : wherefore those Angles are equal . Q. E. D. COROLLARIES . 1. Hence Triangles mutually equilateral ...
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.