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

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Page 271

... with the equimultiples of the second and fourth , according to any multiplication

whatsoever , either both together are less than the second and fourth both

together , or equal taken together , or exceed one the other together , if

... with the equimultiples of the second and fourth , according to any multiplication

whatsoever , either both together are less than the second and fourth both

together , or equal taken together , or exceed one the other together , if

**those**be ... Page 279

... that the Antecedent of one , and the Consequent of the other pair , are in the

same Figure ,

the Ratio is reciprocal in such Figures ; for , reciprocal Figures is unmeaning , In

the ...

... that the Antecedent of one , and the Consequent of the other pair , are in the

same Figure ,

**those**Figures are said to be RECIPROCAL . But more properly ,the Ratio is reciprocal in such Figures ; for , reciprocal Figures is unmeaning , In

the ...

Page 347

I say ,

Line AB , cuting both Planes , H in CD , and EF ; which Lines , neceffarily pass

through the Points A and B , in which the Line AB cuts

.

I say ,

**those**Planes are parallel . Imagine a Plane , CDEF , to pafs through theLine AB , cuting both Planes , H in CD , and EF ; which Lines , neceffarily pass

through the Points A and B , in which the Line AB cuts

**those**Planes , respectively.

Page 2

By Thomas Malton. ... Thomas Malton. In Prob , 20th is hewn how to construct a

Rectangle , equal to Triangle , on

extended to a Trapezium ; or to any Quadrilatéral , whatever , jegular or irregular .

By Thomas Malton. ... Thomas Malton. In Prob , 20th is hewn how to construct a

Rectangle , equal to Triangle , on

**those**Principles ; and in the 22nd it is furtherextended to a Trapezium ; or to any Quadrilatéral , whatever , jegular or irregular .

Page 7

The general Rule for measuring Poligons is , to multiply half the Perimeter , i . e .

half the Sum of all the Sides , by a Perpendicular from the Center to any Side ;

which implies , that a Rectangle of

...

The general Rule for measuring Poligons is , to multiply half the Perimeter , i . e .

half the Sum of all the Sides , by a Perpendicular from the Center to any Side ;

which implies , that a Rectangle of

**those**Dimensions is equal to the Poligon ; the...

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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.