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

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Page 60

To find the Side of a

and Z be the sides of three given Squares . X Y Z It is required to find the

proportion of a Line , on which if a

Area to all ...

To find the Side of a

**Square**, equal to any Number of Squares . Pr . 1o . Let X , Yand Z be the sides of three given Squares . X Y Z It is required to find the

proportion of a Line , on which if a

**Square**be constructed , it shall be equal inArea to all ...

Page 147

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Again ; the

and BD . Then , in the Triangles AIC , CBD , the Sides IC , CA , are equal to BC ...

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Again ; the

**Square**BI is equal to the Rectangle CKLD ; Draw Aland BD . Then , in the Triangles AIC , CBD , the Sides IC , CA , are equal to BC ...

Page 159

If a Line be equally divided , the Rectangle under the Segments is a

is equal to the

equal to four times the

If a Line be equally divided , the Rectangle under the Segments is a

**Square**, andis equal to the

**Square**of either Segment . Hence , the**Square**of a whole Line isequal to four times the

**Square**of half the Line . 4X4X4 = 8x8 , = 64 . THEOREM ... Page 161

ADXBD , or 16x 4 = 64 + the

CFED , i . e . CDO , or 10X10100 or THEOREM VII . ?? E If a Line be divided ,

equally or unequally , at pleasure ; the

ADXBD , or 16x 4 = 64 + the

**Square**IFGH , i . e . CBO , 6x 6 = 36 = the**Square**CFED , i . e . CDO , or 10X10100 or THEOREM VII . ?? E If a Line be divided ,

equally or unequally , at pleasure ; the

**Square**of the whole Line , added to the ... Page 217

To inscribe a

ABCD and EFGH . Draw two Diameters , AC and BD , at Right Angles . Join the

Extremes , A , B , C , D , and a

...

To inscribe a

**Square**in a given Circle ; and to describe a**Square**about a Circle .ABCD and EFGH . Draw two Diameters , AC and BD , at Right Angles . Join the

Extremes , A , B , C , D , and a

**Square**is inscribed . 2nd . Draw Tangents through...

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A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... Thomas Malton No preview available - 2016 |

### 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.