The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 18
... perpendicular to the other . Thus the angles at B are right an- gles . AD is perpendicular to CB , and CB to AD . If the angles formed by D two lines meeting are unequal , the lines are oblique . 4. Two straight lines are parallel when ...
... perpendicular to the other . Thus the angles at B are right an- gles . AD is perpendicular to CB , and CB to AD . If the angles formed by D two lines meeting are unequal , the lines are oblique . 4. Two straight lines are parallel when ...
Página 19
... perpendicular can be erected to the line AB ( ? ) . ( See Def . 3. ) AB ( ? ) . THEOREM II . If two straight lines cut one another , the opposite or ver- tical angles are equal . By Theo . I. , Z + V = 2 right angles . 66 66 " A + V ...
... perpendicular can be erected to the line AB ( ? ) . ( See Def . 3. ) AB ( ? ) . THEOREM II . If two straight lines cut one another , the opposite or ver- tical angles are equal . By Theo . I. , Z + V = 2 right angles . 66 66 " A + V ...
Página 21
... perpendicular to one of two parallels , it is perpendicular to the other ( ? ) . BFG FGD = 2 L's . But , by hypothesis , EF is perpendicular to AB . There- fore , EFB and EFA are right angles ; also ( Theo . II ) , BFG is a right angle ...
... perpendicular to one of two parallels , it is perpendicular to the other ( ? ) . BFG FGD = 2 L's . But , by hypothesis , EF is perpendicular to AB . There- fore , EFB and EFA are right angles ; also ( Theo . II ) , BFG is a right angle ...
Página 23
... perpendicular and oblique lines are drawn from the same point to a given line , the perpendicular is shorter than any oblique line . BH is a perpendicular and BC an oblique line from B to AO . Then , BH is shorter than BC . Continue BH ...
... perpendicular and oblique lines are drawn from the same point to a given line , the perpendicular is shorter than any oblique line . BH is a perpendicular and BC an oblique line from B to AO . Then , BH is shorter than BC . Continue BH ...
Página 24
... perpendicular to another line at its center , is equally distant from the two ends of the line . E G By construction , FE = GE , and BE is perpen- dicular to FG . If by rotation about BE as an axis the point F be made to fall upon G ...
... perpendicular to another line at its center , is equally distant from the two ends of the line . E G By construction , FE = GE , and BE is perpen- dicular to FG . If by rotation about BE as an axis the point F be made to fall upon G ...
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Términos y frases comunes
allel altitude apothegm Axiom Bisect the angles Book chord circle circumference coincide cone construction convex surface diagonal diameter diedral divided draw drawn equal Theo equal to half equally distant equilateral triangle equivalent exterior angle figure frustum Geometry given angle given line given point given straight line half the product Hence hexagon homologous sides hypotenuse hypothesis inscribed inscribed angle intersection isosceles Let ABC measured by half mutually equiangular number of equal number of sides parallel parallelogram parallelopiped pendicular perimeter perpendicular plane polyedron prism Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle secant segment slant height sphere square tangent tetraedron THEOREM THEOREM XI third trapezoid trian triangles ABC triedral vertex
Pasajes populares
Página 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Página 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Página 42 - 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.
Página 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Página 147 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Página 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Página 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.
Página 39 - The area of a rectangle is equal to the product of its base and altitude.