Elements of the Geometry of Planes and Solids: With Four PlatesThe author, 1828 - 159 páginas |
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Página 5
... ratio and proportion , as there explained . It will be proper here to give a clear idea of the distinct na- ture of the different propositions made use of in Geometry , their parts , and the principles of their modes of demonstration ...
... ratio and proportion , as there explained . It will be proper here to give a clear idea of the distinct na- ture of the different propositions made use of in Geometry , their parts , and the principles of their modes of demonstration ...
Página 71
... ratio of the squares of their sides opposite to equal angles , or what is called homolo- gous sides . For every parallelogram that resulted being discom- ponible in as many triangles equal to the AaD , there will be found in each of the ...
... ratio of the squares of their sides opposite to equal angles , or what is called homolo- gous sides . For every parallelogram that resulted being discom- ponible in as many triangles equal to the AaD , there will be found in each of the ...
Página 72
... ratio as their bases . APPLIC . If the triangles ABC , and DEF , ( fig . 68 , ) have the same altitude , that is : that they are , or can be , between the same parallels ; these triangles will have to one another the same ratio as their ...
... ratio as their bases . APPLIC . If the triangles ABC , and DEF , ( fig . 68 , ) have the same altitude , that is : that they are , or can be , between the same parallels ; these triangles will have to one another the same ratio as their ...
Página 73
... ratio , but that they were to another as AB , to Df , smaller ( or greater ) than DE ; find a subdivision of AB , so that the parts be smaller than fE , and suppose them laid off in DE , until one of the subdivisions fall between f ...
... ratio , but that they were to another as AB , to Df , smaller ( or greater ) than DE ; find a subdivision of AB , so that the parts be smaller than fE , and suppose them laid off in DE , until one of the subdivisions fall between f ...
Página 74
... ratio to one another ; and inversely , if two sides of a triangle are cut propor- tionally , the cutting line will be parallel to the third line . APPLIC . Let the sides AB , AC , ( fig . 69 , ) or their pro- traction on either side of ...
... ratio to one another ; and inversely , if two sides of a triangle are cut propor- tionally , the cutting line will be parallel to the third line . APPLIC . Let the sides AB , AC , ( fig . 69 , ) or their pro- traction on either side of ...
Otras ediciones - Ver todas
Elements of the Geometry of Planes and Solids: With Four Plates Ferdinand Rudolph Hassler Vista de fragmentos - 1828 |
Elements of the Geometry of Planes and Solids: With Four Plates (Classic ... F. R. Hassler Sin vista previa disponible - 2018 |
Términos y frases comunes
ABCD angle equal angle G angles opposite angular point APPLIC base and altitude bisect centre chord circumference circumscribed circle common intersection cone Corol cutting line cylinder Demonstr describe determine diagonal diameter draw drawn equal angles equal base equal sides equiangular equilateral triangle four right angles frustum given angle given circle given lines given point given straight line given triangle gles greater inner angles inscribed join line BC opposite angles parallel planes parallelepiped parallelogram perpendicular plane angles Plane Geometry point of intersection prisms PROBLEM Proof proportional protracted pyramid quadrilateral figure radii radius ratio rectilineal figure regular poligon Scholium segment side AC similar similar triangles six right solid angle solid content sphere square subtended supposition surface tangent thence THEOREM third plane third side three plane three sides triangle ABC triangular vertex
Pasajes populares
Página 44 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...
Página 20 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 11 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 2 - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Página 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 119 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 61 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Página 113 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Página 29 - EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (I.
Página 16 - E the centre of the circle, and join EA, EB. Then, because AF is equal to FB, and FE common to the two triangles AFE, BFE, there are two sides in the one, equal to two sides in the other, and the base EA is equal to the base EB; therefore the angle AFE is equal...