A Treatise on Special Or Elementary Geometry, Bände 1-2Sheldon, 1872 - 1 Seiten |
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Seite 61
... DEM . - Let the two lines AB and CD intersect at right angles at E ; and let the portion of the plane of the lines on the side of CD on which B lies be conceived to revolve on the line CD as an axis , † until it falls in the * When a ...
... DEM . - Let the two lines AB and CD intersect at right angles at E ; and let the portion of the plane of the lines on the side of CD on which B lies be conceived to revolve on the line CD as an axis , † until it falls in the * When a ...
Seite 62
... let fall upon that line , and only one . DEM . - Let AB be any line , and P any point without the line ; then one per- pendicular , and only one , can be let fall from P upon AB . F DE CB FIG . 105 . For , conceive any oblique line , as ...
... let fall upon that line , and only one . DEM . - Let AB be any line , and P any point without the line ; then one per- pendicular , and only one , can be let fall from P upon AB . F DE CB FIG . 105 . For , conceive any oblique line , as ...
Seite 66
... DEM . - Let AB and CE intersect at D ; then CDA = the opposite angle BDE , ADE = the opposite or vertical angle CDB , and ADC + CDB + BDE + EDA = four right angles . For , since CD meets AB , ADC + CDB = two right angles ( 131 ) . Also ...
... DEM . - Let AB and CE intersect at D ; then CDA = the opposite angle BDE , ADE = the opposite or vertical angle CDB , and ADC + CDB + BDE + EDA = four right angles . For , since CD meets AB , ADC + CDB = two right angles ( 131 ) . Also ...
Seite 67
... DEM . - Let AB be any straight line , P any point without it , PD a perpen- dicular , and PC and PE oblique lines cutting AB at C and E , so that DC = DE ; then PC = PE , angle CPD angle DPE , and angle PCD = angle PED . * Revolve the ...
... DEM . - Let AB be any straight line , P any point without it , PD a perpen- dicular , and PC and PE oblique lines cutting AB at C and E , so that DC = DE ; then PC = PE , angle CPD angle DPE , and angle PCD = angle PED . * Revolve the ...
Seite 68
... let fall on the line , and two oblique lines be drawn , the oblique line which cuts off the greater distance from the foot of the perpendicular is the greater . DEM . - Let AB be any straight line , P any point without it , and PC and ...
... let fall on the line , and two oblique lines be drawn , the oblique line which cuts off the greater distance from the foot of the perpendicular is the greater . DEM . - Let AB be any straight line , P any point without it , and PC and ...
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A Treatise on Special Or Elementary Geometry: In Four Parts Edward Olney Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
ABCD adjacent altitude angle or arc bisect centre chord circle circumference coincide common point conceive construct cosec cosine cotangent DEM.-Let diagonals diameter diedral distance divided draw drawn equal angles equiangular equilateral equivalent exterior angle facial angles figure frustum geometrical given line given point Hence hypotenuse included angle inscribed intersect isosceles less let fall locus LOGARITHMIC FUNCTIONS lune measured middle point number of sides parallel parallelogram parallelopiped passing pendicular perpendicular plane triangle prism Prob Prob.-To produced project the triangle PROP PROPOSITION pyramid quadrant quadrilateral radii radius rectangle regular polygon revolve right angled triangle secant secant line similar similar triangles sine solution sphere spherical angle spherical triangle square straight line student SUG's surface symmetrical tang tangent Theorem.-The triangle ABC triedral trigonometrical trigonometrical functions values vertex vertices whence
Beliebte Passagen
Seite 219 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 111 - If the diagonals of a parallelogram are equal, the figure is a rectangle.
Seite 130 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Seite 33 - Cut out two such triangles and try it Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on the other ? Try it. Ex. 7. If you have two triangles with two sides in one equal respectively to two sides in the other, and the included angle in one greater than in the other, how is it with the third sides of the triangles ? 76.
Seite 109 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Seite 106 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Seite 250 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Seite 245 - If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them.
Seite 141 - Hence, the area of a trapezoid is equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel.
Seite 81 - In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM. — Let CE < AB, then is the perpendicular OD, which measures the distance of CE from the centre, greater than OD' •which measures the distance of AB from the centre.