## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

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Page 48

B E Е Pr.4 O A

given Angle , cuting BC in E , by Produce BC ; and draw DF parallel to AE . - 5 .

The Parallelogram AEFD is equal to the given Rectangle

B E Е Pr.4 O A

**ABCD**is the given Rectangle . F Make the Angle DAE equal to thegiven Angle , cuting BC in E , by Produce BC ; and draw DF parallel to AE . - 5 .

The Parallelogram AEFD is equal to the given Rectangle

**ABCD**. . P. 18. I. Or , it ... Page 143

In the Parallelogram

and ED : The Triangle DEC is equal half the Parallelogram ,

parallel to AD and BC . Dem . The Parallelograms , AEFD and FEBC , are

bisected ...

In the Parallelogram

**ABCD**, affume any Point , E , in the Side AB , and draw ECand ED : The Triangle DEC is equal half the Parallelogram ,

**ABCD**. Draw EF ,parallel to AD and BC . Dem . The Parallelograms , AEFD and FEBC , are

bisected ...

Page 144

B В с F Th . 15 Ax . The Parallelogram

; standing on the same Base A D ; and between the same Parallels AH , BG ; i . e

. they have the same.or equal Altitudes . Also , the Par .

B В с F Th . 15 Ax . The Parallelogram

**ABCD**is equal to the Parallelogram AFGD; standing on the same Base A D ; and between the same Parallels AH , BG ; i . e

. they have the same.or equal Altitudes . Also , the Par .

**ABCD**is equal to EFGH ... Page 391

Let the Pyramids

being fimilar , are each equal to the third part of a Prism on the same Base and

Altitude . But , Quantities are in the same Ratio , to each other , as their ...

Let the Pyramids

**ABCD**,**abcd**be similar . ( Fig . 2. ) The Pyramids**ABCD**,**abcd**,being fimilar , are each equal to the third part of a Prism on the same Base and

Altitude . But , Quantities are in the same Ratio , to each other , as their ...

Page 5

.

only . For , it is demonstrable , that , the Triangle AGE = DHF . 7.1 . Consequently

...

**ABCD**. For , if AE be multiplied into AD , it will produce an Area equal to the Rect.

**ABCD**, because , AB = AE . But , the Par . AEFD is equal to the Rect . AGHDonly . For , it is demonstrable , that , the Triangle AGE = DHF . 7.1 . Consequently

...

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### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.