The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page 27
... Base are always acute . 12. In an equilateral Triangle , each Angle is two thirds of a right Angle . For it is one third of two right ones , therefore it is two thirds of one right one . 13. Hence a right Angle ( B A C ) is eafily ...
... Base are always acute . 12. In an equilateral Triangle , each Angle is two thirds of a right Angle . For it is one third of two right ones , therefore it is two thirds of one right one . 13. Hence a right Angle ( B A C ) is eafily ...
Page 32
... Base , one of them be extended unto an infinite Length , it ftill remains but equal to the other , by the Force of the present Demon- Atration . [ From hence it follows , that two Cities in Magnitude equal , may fo much differ in ...
... Base , one of them be extended unto an infinite Length , it ftill remains but equal to the other , by the Force of the present Demon- Atration . [ From hence it follows , that two Cities in Magnitude equal , may fo much differ in ...
Page 35
... 35. Fig . 65 . we learn that the Area of whatfoever Triangle , as AFB , is produced from half the Altitude FI multi- plied into the Base A B , or half the Bafe multiplied D 2 into Fig . 66 . Per 31 . ( b ) Lib . I. 35 EUCLID'S Elements .
... 35. Fig . 65 . we learn that the Area of whatfoever Triangle , as AFB , is produced from half the Altitude FI multi- plied into the Base A B , or half the Bafe multiplied D 2 into Fig . 66 . Per 31 . ( b ) Lib . I. 35 EUCLID'S Elements .
Page 36
... Base 50 by 85 , and you have the Area of the Triangle AFB - 4250 Feet Square . Further , the Altitude of a Triangle , when the Area of it is in all Points acceffible , may be known mechanically as well as the Sides . But if the Area of ...
... Base 50 by 85 , and you have the Area of the Triangle AFB - 4250 Feet Square . Further , the Altitude of a Triangle , when the Area of it is in all Points acceffible , may be known mechanically as well as the Sides . But if the Area of ...
Page 60
... Base , is perpendicular to it . And on the contrary , a Line which falling from the Top of the Angle is perpendicular to the Bafe , doth bfect it . ( 2. ) Hence it follows , that half of the Chord of every Arch , is the right Sine of ...
... Base , is perpendicular to it . And on the contrary , a Line which falling from the Top of the Angle is perpendicular to the Bafe , doth bfect it . ( 2. ) Hence it follows , that half of the Chord of every Arch , is the right Sine of ...
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The Elements of Euclid: With Select Theorems Out of Archimedes Archimedes,André Tacquet,Euclid No preview available - 2015 |
Common terms and phrases
alfo alfo equal alſo Altitude Arch Archimedes Axis Bafe Baſe becauſe betwixt themſelves bifected Centre Circum circumfcrib'd Circumference confequently Conftruction conical Superficies conical Surfaces contain'd Coroll Corollary Cylinder defcrib'd defcribe demonftrated Diameter double drawn thro equal Angles equilateral Cone equilateral Triangle Euclid faid fame manner fcrib'd fecond felf fhall be equal fhew fhew'd Figure firft firſt folid Angle fome fore foregoing four right ftand fuppos'd given right Line greater hath Height Hypothefis infcrib'd infcribed Interfections leffer lefs likewife Line BC manifeft Mathematicks mean Proportional betwixt Meaſure Number oppofite pafs thro parallel Parallelepiped Parallelogram Pentagon perpendicular Plane Point Polygon Prifm Priſms Proclus produc'd PROP Propofition Pyramids Radius Rectangle right Angle right Line Scholium Segment Semidiameter Solid Sphere Square thefe Theorem theſe Thing thofe unto whatſoever whofe whole Superficies
Popular passages
Page 21 - 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.
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Page 11 - Because the angle A is equal to the angle C, and the angle...
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Page xix - How great a Geometrician art thou, O Lord! For while this Science has no Bounds, while there is for ever room for the Discovery of New Theorems, even by Human Faculties; Thou art acquainted with them all at one View, without any Chain of Consequences, without any Fatigue of Demonstrations.
Page 211 - Side next to the Diameter : and let the right Lines BH, CG, DF, join the Angles which are equally diftant from A. I fay that the...
Page 221 - Axis, is alfo given j it is manifeft that each of the Segments become known. Now both the foregoing, and all the reft of the Theorems which follow...