The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 páginas |
Dentro del libro
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Página 15
... perimeter of a polygon is the sum of the lines which bound it . The perimeter of a circle is its circum- ference . Postulates . 1. Let it be granted that a straight line may be drawn from any point to any other point ; 2. That a ...
... perimeter of a polygon is the sum of the lines which bound it . The perimeter of a circle is its circum- ference . Postulates . 1. Let it be granted that a straight line may be drawn from any point to any other point ; 2. That a ...
Página 130
... perimeters of similar polygons are proportional to their homologous sides ( IV . 16 ) . 5. A line drawn parallel to the parallel sides of a trapezoid will cut the other sides proportionally . 6. If two triangles be on equal bases and ...
... perimeters of similar polygons are proportional to their homologous sides ( IV . 16 ) . 5. A line drawn parallel to the parallel sides of a trapezoid will cut the other sides proportionally . 6. If two triangles be on equal bases and ...
Página 131
... perimeter mul- tiplied by the radius of the inscribed circle . For other practical problems in this book see Mensuration at the end of Book VI . BOOK VI . REGULAR POLYGONS . - MEASUREMENT OF THE GEOMETRY . - BOOK V. 131 BOOK VI.
... perimeter mul- tiplied by the radius of the inscribed circle . For other practical problems in this book see Mensuration at the end of Book VI . BOOK VI . REGULAR POLYGONS . - MEASUREMENT OF THE GEOMETRY . - BOOK V. 131 BOOK VI.
Página 139
... perimeter and apothem . Let ABC be a polygon and DE its apothem ; then the area of ABC is equal to ( AB + BF + FC + CG + GH + HA ) ED . Join ᎠᎪ , ᎠᏴ , etc .; H the area of the triangle DAB is equal to ( V. 16 , Cor . 2 ) AB ED . But ...
... perimeter and apothem . Let ABC be a polygon and DE its apothem ; then the area of ABC is equal to ( AB + BF + FC + CG + GH + HA ) ED . Join ᎠᎪ , ᎠᏴ , etc .; H the area of the triangle DAB is equal to ( V. 16 , Cor . 2 ) AB ED . But ...
Página 140
... perimeter of the circumscribed and p of the in- scribed polygon , then the differ- E C ence of the polygons - that is , the sum of all trapezoids , AF , etc. —is ( P + p ) HG , and is therefore less than P × HG . Now because DG + GA ...
... perimeter of the circumscribed and p of the in- scribed polygon , then the differ- E C ence of the polygons - that is , the sum of all trapezoids , AF , etc. —is ( P + p ) HG , and is therefore less than P × HG . Now because DG + GA ...
Otras ediciones - Ver todas
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Sin vista previa disponible - 2016 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Sin vista previa disponible - 2017 |
Términos y frases comunes
A-BCD AB² ABCD altitude angle ABC angle ACB angle BAC apothem bisect centre of similitude chord circle ABC circumference cone Corollary cylinder decagon describe diagonals diameter divided draw equal angles equiangular feet figure four right angles frustum given circle given straight line greater Hence inscribed interior angles intersect isosceles Let ABC line joining lune meet middle point multiplied number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism produced Prop proportional Proposition 12 Proposition 13 pyramid quadrilateral radical axis radii radius rectangle contained regular polygon right angles Scholium segment semicircle similar similar triangles slant height solid solid angle sphere spherical triangle square surface symmetrical tangent Theorem Theorem.-If three sides triangle ABC vertex
Pasajes populares
Página 53 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 81 - On 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 31 - Any two angles of a triangle are together less than two right angles.
Página 128 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.
Página 82 - To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle. Let ABC be the given circle, and D the given rectilineal angle ; it is required to cut off a segment from the circle ABC that shall contain an angle equal to the given angle D.
Página 62 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Página 166 - A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB: these together are less than four right angles. Let the planes...
Página 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.
Página 120 - Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.