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

### From inside the book

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Page 68

А Y B X N But , if the Proportional was required to be to Z , as Y to X ; then the

Rectangle , or any Parallelogram , ABCD ,

which will , in this Cafe , be the two Means ; and DG the Proportional fought , is

now ...

А Y B X N But , if the Proportional was required to be to Z , as Y to X ; then the

Rectangle , or any Parallelogram , ABCD ,

**must**be under the two Lines Y and Z ;which will , in this Cafe , be the two Means ; and DG the Proportional fought , is

now ...

Page 118

2 ABC ; or 2 ABO ;

and , 2 or 3 AB a Square

Triangle . Thus , AABC , fignifies the Triangle ABC . A X I 0 MS . Ι An Axiom ( as ...

2 ABC ; or 2 ABO ;

**must**be read , two Rectangles ABC , or twice the Rect . AB ;and , 2 or 3 AB a Square

**must**be understood , twice or thrice the Square of AB . ATriangle . Thus , AABC , fignifies the Triangle ABC . A X I 0 MS . Ι An Axiom ( as ...

Page 179

For , if the Circles , AD and BD , touched inwardly , in more than a Point , as at D ,

the Curve of the lesser Circle , AD ,

curve of the larger Circle , BD , which , from the genefis of a Circle ; cannot be ...

For , if the Circles , AD and BD , touched inwardly , in more than a Point , as at D ,

the Curve of the lesser Circle , AD ,

**must**coincide in some part , entirely , with thecurve of the larger Circle , BD , which , from the genefis of a Circle ; cannot be ...

Page 339

These things

what is intended , can poflibly follow . I thought it necessary to apprise the young

Student of these preliminaries ; otherwise ( without a Tutor ) he would , frequently

...

These things

**must**be granted and understood to be fo , or no Demonstration , ofwhat is intended , can poflibly follow . I thought it necessary to apprise the young

Student of these preliminaries ; otherwise ( without a Tutor ) he would , frequently

...

Page 9

But , the greater the number of Sides of the Poligon , the nearer it is to the Area of

the Circle , i.e. to the Circle itself ; and consequently , it

Circle ; that is , the Perimeter of the Poligon , will be equal to the Circumference of

...

But , the greater the number of Sides of the Poligon , the nearer it is to the Area of

the Circle , i.e. to the Circle itself ; and consequently , it

**must**at last end in theCircle ; that is , the Perimeter of the Poligon , will be equal to the Circumference of

...

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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.