## Primary Elements of Plane and Solid Geometry: For Schools and Academies |

### Inni boken

Side 27

III ) ; also , since it intersects the parallels AB , DC , the alternate angles BAC ,

DCA , are equal . Hence , the two triangles ABC , ADC ,

are ...

III ) ; also , since it intersects the parallels AB , DC , the alternate angles BAC ,

DCA , are equal . Hence , the two triangles ABC , ADC ,

**have two angles of the****one equal to two angles of the other**, and the included side AC common ; theyare ...

Side 67

Now , since the triangles ABF , abf ,

ab ? ( Theo . VIII ) . Multiplying an extreme and a mean equally , 5 ABF : 5 abf : :

ABP ...

Now , since the triangles ABF , abf ,

**have two angles of the one equal to two****angles of the other**, they are similar ( Cor . , Theo . III ) ; hence , ABF : abf : : ABP :ab ? ( Theo . VIII ) . Multiplying an extreme and a mean equally , 5 ABF : 5 abf : :

ABP ...

Side 69

...

consequently similar ( Cor . , Theo . III ) . Therefore , AC : AB : : AB : AD . That is , if

from a point , etc. arc THEOREM XIV . AM It may Similar arcs in different BOOK II .

69.

...

**have two angles of the one equal to two angles of the other**, and areconsequently similar ( Cor . , Theo . III ) . Therefore , AC : AB : : AB : AD . That is , if

from a point , etc. arc THEOREM XIV . AM It may Similar arcs in different BOOK II .

69.

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Primary Elements of Plane and Solid Geometry: For Schools and Academies Evan Wilhelm Evans Uten tilgangsbegrensning - 1862 |

Primary Elements of Plane and Solid Geometry: For Schools and Academies E. W. 1827-1874 Evans Ingen forhåndsvisning tilgjengelig - 2016 |

Primary Elements of Plane and Solid Geometry: For Schools and Academies Evan Wilhelm Evans Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

altitude base Book called chord circle circumference coincide common cone consequently containing convex surface DEFINITIONS describe diameter direction divided draw drawn ECLECTIC equal equal Theo equal to half equilateral equivalent exercises extreme faces fall feet figure follows frustum Geometry given greater half the product Hence hypotenuse included angle inscribed intersect Join length less Let ABCD magnitudes manner McGuffey's mean measured by half meet multiplied mutually opposite parallel parallelogram parallelopiped perimeter perpendicular plane polygon prism PROBLEM proportion proved pyramid radius ratios Ray's rectangle regular polygon remainder respectively right angles Schol SERIES shown sides similar slant hight solidity Solution sphere square straight line taken Theo THEOREM third triangle triangles ABC unit vertex whole

### Populære avsnitt

Side 69 - 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.

Side 42 - 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.

Side 21 - 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 are equal in all respects.

Side 47 - It follows, then, that the area of a circle is equal to half the product of its circumference and its radius.

Side 72 - 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

Side 33 - 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.

Side 38 - The area of a regular polygon is equal to half the product of its apothem and perimeter.

Side 52 - PROBLEM VII. Two angles of a triangle being given, to find the third angle. The three angles of every triangle are together equal to two right angles (Prop.

Side 30 - The area of a rectangle is equal to the product of its base and altitude.

Side 69 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...