## Elements of Geometry |

### From inside the book

Results 6-10 of 60

Page 48

...

...

**altitude**EF by half the sum of the sides AB , CD , which may be expressed in this manner ; ABCD = EFX ᎯᏴ ( AB + CD ) . 2 179. Scholium . If through the point I , the middle of BC , IH be drawn parallel to the base AB , the point H ... Page 50

...

...

**altitude**AE is the difference of these lines ; therefore the rectangle AKLE = ( AB + BC ) × ( AB — BC ) . But this same rectangle is composed of two parts ABHE + BHLK , and the part BHLK is equal to the rectangle EDGF , for BH = DE ... Page 51

...

...

**altitude**BF , the square BCGF is to the rectangle BDEF as the base BC is to the base BD ; therefore -2 BC : AB :: BC : BD , or , the square of the hypothenuse is to the square of one of the sides of the right angle , as the hypothenuse ... Page 52

...

...

**altitude**DE , are to each other as their bases BD , CD . Now these rectangles are equivalent to the squares AH , AI , therefore , 2 -2 AB : AC :: BD : DC , or , the squares of the two sides of a right angle are to each other , as the ... Page 54

...

...

**altitude**, since the vertices B and C are situated in a parallel to the base ; therefore the triangles are equivalent ( 170 ) . The triangles ADE , BDE , of which the common vertex is E , have the same**altitude**, and are to each other ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence