Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
From inside the book
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Page 19
... also bisect the given Line AB . For AC = BC , and the Side CD is com- mon , and the AngleACD = BCD : There- fore d AD = BD . Q. E. F. The Construction of Prop . 1. of this Book is sufficient for shewing the Practice of this , and the ...
... also bisect the given Line AB . For AC = BC , and the Side CD is com- mon , and the AngleACD = BCD : There- fore d AD = BD . Q. E. F. The Construction of Prop . 1. of this Book is sufficient for shewing the Practice of this , and the ...
Page 26
... also be greater than the Base ( bc ) of the other . Make the a Angle bag equal to A , and the Side ag = ac , and join bg , cg . b : Cafe 1. When bg falls above bc , then because ABdab , and AC = ag , and the Angle A = a ; therefore is ...
... also be greater than the Base ( bc ) of the other . Make the a Angle bag equal to A , and the Side ag = ac , and join bg , cg . b : Cafe 1. When bg falls above bc , then because ABdab , and AC = ag , and the Angle A = a ; therefore is ...
Page 28
... also the Angle Ad = bac . Q. E. D. Hyp . 2. Let AB = ab ; I tay , BC = bc , and AC = ac , and the Angle A = bac . For if you fay that be BC , make be BC , and join ae . Because AB = ab , and BC = be , and the Angle Bg = 6 : therefore ...
... also the Angle Ad = bac . Q. E. D. Hyp . 2. Let AB = ab ; I tay , BC = bc , and AC = ac , and the Angle A = bac . For if you fay that be BC , make be BC , and join ae . Because AB = ab , and BC = be , and the Angle Bg = 6 : therefore ...
Page 29
... contrary to the Hypothesis.f 13 ax . But also the Ang . DHG + CHG = twog 13. 1 . right Angles : Therefore DHG = AGH h 3 ax . CO_1 15.1 . BGE . Q.E. D. COROL . B C Hence every Paralle- logram ( AC Book I. EUCLID'S Elements . 29.
... contrary to the Hypothesis.f 13 ax . But also the Ang . DHG + CHG = twog 13. 1 . right Angles : Therefore DHG = AGH h 3 ax . CO_1 15.1 . BGE . Q.E. D. COROL . B C Hence every Paralle- logram ( AC Book I. EUCLID'S Elements . 29.
Page 30
... also parallel the one to the C T D other . Let the Line GI cut the three given Lines any how ; then because AB , EF are parallel , the Angle C 29.1 . AGI will be = EHI : also because CD and 1 EF are parallel , the Angle EHI will be diax ...
... also parallel the one to the C T D other . Let the Line GI cut the three given Lines any how ; then because AB , EF are parallel , the Angle C 29.1 . AGI will be = EHI : also because CD and 1 EF are parallel , the Angle EHI will be diax ...
Common terms and phrases
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe Baſe Base BC becauſe biſect Center Circ Circle Circumference Cone conft Conſequent COROL Cylinder demonſtrated deſcribed Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples faid fame fimilar fince firſt folid fore four right given right Line gles Gnomon greater Hence leſs likewiſe Line CD Magnitudes manifeſt Number oppofite parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular Point Polyhedron Priſm Probl Proportion Pyramids Q. E. D. PROP Ratio Reaſon Rectangle right Angles right Line AB right Line AC right-lined Figure ſaid ſame ſay SCHOL SCHOLIU ſecond Segment ſhall Side BC ſince ſome Sphere Square ſtand ſuppoſe theſe thoſe tiple Triangle ABC triplicate Whence whole whoſe
Popular passages
Page 29 - 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 143 - 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 31 - 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 25 - 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 29 - 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 217 - ... to one of the consequents, so are all the antecedents to all the consequents ; [V. 12] hence the whole polyhedral solid in the sphere about A as centre has to the whole polyhedral solid in the other sphere the ratio triplicate of that which AB has to the radius of the other sphere, that is, of that which the diameter BD has to the diameter of the other sphere. QED This proposition is of great length and therefore requires summarising in order to make it easier to grasp. Moreover there are some...
Page 9 - 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.
Page 217 - And as one antecedent is to its confequent, fo are all the antecedents to all the confequents. Wherefore the whole folid polyhedron in the greater fphere has to the whole folid polyhedron in the other, the triplicate ratio of that which AB...
Page 217 - Center is A, to every one of the Pyramids of the fame Order in the other Sphere, hath a triplicate Proportion of that which AB has to that Line drawn from the Center of the other Sphere.