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

### From inside the book

Results 1-5 of 5

Page

Article Page - 7 10 Į . How the

Rectangle whatever . 3. Of the Triangle . 4 4. All Figures , having equal circuit ,

are not equal in

Rectangle , the ...

Article Page - 7 10 Į . How the

**Area**of a Square is obtained . 3 2. Of anyRectangle whatever . 3. Of the Triangle . 4 4. All Figures , having equal circuit ,

are not equal in

**Area**. 5. A Square contains a grea er**Area**than any otherRectangle , the ...

Page 3

How the

Triangle . 4 4. All Figures , having equal circuit , are not equal in

Square contains a grea er

How the

**Area**of a Square is obtained . 3 2. Of any Rectangle whatever . 3. Of theTriangle . 4 4. All Figures , having equal circuit , are not equal in

**Area**. 4 5. ASquare contains a grea er

**Area**than any other 5 Rectangle , the sums of whose ... Page 3

Hence it is plain , that a Rectangle contains a greater

Quadrilateral whatever ; if the meafure of their Side , in one Sum , be equal . But ,

a Square , which is the most perfect Rectangle , contains a less

regular ...

Hence it is plain , that a Rectangle contains a greater

**Area**than any otherQuadrilateral whatever ; if the meafure of their Side , in one Sum , be equal . But ,

a Square , which is the most perfect Rectangle , contains a less

**Area**than aregular ...

Page 5

For , if AE be multiplied into AD , it will produce an

, because , AB = AE . But , the Par . AEFD is equal to the Rect . AGHD only . For ,

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

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 . AGHD only . For ,

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

Page 6

The

Rectangle is but 8 x6 = 48 ; one 49th part less , in its

which is accounted for by the Figure ; and from the 11th Theorem , Book 5th ,

Hence , it is ...

The

**area**of the Square is 7 x7 ; or 7 times 7 = 49 , whereas the**area**of theRectangle is but 8 x6 = 48 ; one 49th part less , in its

**Area**, than the Square ;which is accounted for by the Figure ; and from the 11th Theorem , Book 5th ,

Hence , it is ...

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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.