## 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 129

Hence , if two sides of one Triangle be equal , respectively , to two sides of

another Triangle , and the contained Angle , of one , be greater or

contained Angle of the other , the remaining Side will allo be greater or

...

Hence , if two sides of one Triangle be equal , respectively , to two sides of

another Triangle , and the contained Angle , of one , be greater or

**less**than thecontained Angle of the other , the remaining Side will allo be greater or

**less**; and...

Page 188

AG is

greater than AC . But , GC is equal to HC ; wherefore , AC - GC , i.e. AG , is

than AH - Ax.8.1 . 4th . AH is

...

AG is

**less**than AH or Al . Draw CH and CI . Then , in the Tri . ACH ; AH + HC isgreater than AC . But , GC is equal to HC ; wherefore , AC - GC , i.e. AG , is

**less**than AH - Ax.8.1 . 4th . AH is

**less**than Al , which falls further from $ C . For , in the...

Page 257

whether the first be equal Bto , greater , or

also equal to , greater , or

equal to B , C = D ; and , if A be greater , or

whether the first be equal Bto , greater , or

**less**than the second , the third is aalso equal to , greater , or

**less**than the fourth . DIf A : B :: C : D ; then , if A beequal to B , C = D ; and , if A be greater , or

**less**than B ; C is , also , A greater , or**less**... Page 273

It is certain , that being multiplied , mentally , according to this Definition , if they

were analogous , the Antecedents would be either greater or

Consequents , contie nually , but never equal ; for if , by taking Equimultiples ,

they ...

It is certain , that being multiplied , mentally , according to this Definition , if they

were analogous , the Antecedents would be either greater or

**less**than theConsequents , contie nually , but never equal ; for if , by taking Equimultiples ,

they ...

Page 9

This Poligon is greater than the Decagon , by ten Ifosceles Triangles , equal AGI ,

in the Segment AG or GB ; and it is itill

or IG . 9. From all which , it is clear , that every Poligon , inscribed in a Circle , is ...

This Poligon is greater than the Decagon , by ten Ifosceles Triangles , equal AGI ,

in the Segment AG or GB ; and it is itill

**less**than the Circle by twenty Seginents Alor IG . 9. From all which , it is clear , that every Poligon , inscribed in a Circle , is ...

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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.