Mrs. Annie Griswold Fordyce Marsh Horace Wilmer Marsh.

Constructive text-book of practical mathematics, Volume 2, Part 1 online

. (page 21 of 22)
Online LibraryMrs. Annie Griswold Fordyce Marsh Horace Wilmer MarshConstructive text-book of practical mathematics, Volume 2, Part 1 → online text (page 21 of 22)
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Cotangent


Angle


o /

14 00


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


76 00


.2419 9.3837


.9703 9.9869


.2493 9.3968


4.0108 0.6032


10


.2447 3887


.9696 9866


.2524 4021


3.9617 5979


60


20


. 2476 3937


.9689 9863


.2555 4074


3.9136 5926


40


30


.2504 3986


.9681 9859


.2586 4127


3.8667 5873


30


40


.2532 4035


.9674 9856


.2617 4178


3.8208 5822


20


50


.2560 4083


.9667 9853


.2648 4230


3.7760 5770


10


15 00


.2588 9.4130


.9659 9.9849


.2679 9.4281


3.7321 0.5719


75 00


10


.2616 4177


.9652 9846


.2711 4331


3.6891 5669


50


20'


.2644 4223


.9644 9843


.2742 4381


3.6470 5619


40


30


. 2672 4269


.9636 9839


. 2773 4430


3.6059 5570


30


40


.2700 4314


.9628 9836


.2805 4479


3.5656 5521


20


50


.2728 4359


.9621 9832


.2836 4527


3.5261 6473


10


16 00


.2756 9.4403


.9613 9.9828


.2867 9.4575


3.4874 0.6325


74 00


10


.2784 4447


.9605 9825


.2899 4622


3.4495 6378


50


20


.2812 4491


.9596 9821


.2931 4669


3.4124 5331


40


30


.2840 4533


.9588 9817


.2962 4716


3.3759 5284


30


40


.2868 4576


.9580 9814


.2994 4762


3.3402 5238


20


50


.2896 4618


.9572 9810


.3026 4808


3.3052 6192


10


17 00


.2924 9.4659


.9563 9.9806


.3057 9.4853


3.2709 0.6147


73 00


10


.2952 4700


.9555 9802


.3089 4898


3.2371 6102


50


20


.2979 4741


.9546 9798


.3121 4943


3.2041 6057


40


30


.3007 4781


.9537 9794


.3153 4987


3.1716 5013


30


40


.3035 4821


.9528 9790


.3185 5031


3.1397 4969


20


60


.3062 4861


.9520 9786


.3217 5076


3.1084 4925


10


18 00


.3090 9.4900


.9511 9.9782


.3249 9.6118


3.0777 0.4882


72 00


10


.3118 4939


.9502 9778


.3281 5161


3.0475 4839


50


20


.3145 4977


.9492 9774


.3314 5203


3.0178 4797


40


30


.3173 5015


.9483 9770


.3346 5245


2.9887 4755


30


40


.3201 5052


.9474 9765


.3378 5287


2.9600 4713


20


50


.3228 5090


.9466 9761


.3411 6329


2.9319 4671


10


19 00


.3256 9.5126


.9455 9.9757


.3443 9.6370


2.9042 0.4630


71 00


10


.3283 5163


.9446 9752


.3476 6411


2.8770 4589


50


20


.3311 5199


.9436 9748


.3508 6451


2.8502 4549


40


30


.3338 5235


.9426 9743


.3641 5491


2.8239 4509


30


40


.3365 5270


.9417 9739


.3574 5531


2.7980 4469


20


50


.3393 5306


.9407 9734


.3607 5571


2.7725 4429


10


20 00


.3420 9.5341


.9397 9.9730


.3640 9.5611


2.7475 0.4389


70 00


10


.3448 5375


.9387 9725


.3673 5650


2.7228 4350


50


20


. 3475 5409


.9377 9721


.3706 5689


2.6985 4311


40


30


.3502 6443


.9367 9716


.3739 5727


2.6746 4273


30


40


.3529 5477


.9356 9711


.3772 5766


2.6511 4234


20


50


.3557 6510


.9346 9706


.3805 5804


2.6279 4196


10


21 00

O '


.3584 9.5543


.9336 9.9702


.3830 9.5842


2.6051 0.4158


69 00

o /


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


Angle


Cosine


Sine


Cotangent


Tangent


Angle



Digitized by VjOOQIC



408



REFERENCE TABLES



TABLE Xll.— Continued



Anolb


SlNB


COBINB


Tangent


Cotangent


Angle


•o /

21 00


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


O f

69 00


.3584 9.5543


.9336 9.9702


.3839 9.5842


2.6051 0.4158


10


.3611 5576


.9325 9697


.3872 5879


2.5826 4121


50


20


.3638 5600


.9315 9692


.3906 5917


2.5605 4083


40


30


.3665 5641


.9304 9687


.3939 5954


2.5386 4046


30


40


.3692 5673


.9293 9682


.3973 5991


2.5172 4009


20


50


.3719 5704


.9283 9677


.4006 6028


2.4960 3972


10


22 00


.3746 9.5736


.9272 9.9672


.4040 9.6064


2.4751 0.3936


68 OO


10


.3773 5767


.9261 9667


.4074 6100


2.4545 3900


50


20


.3800 5798


.9250 9661


.4108 6136


2.4342 3864


40


30


.3827 5828


.9239 9656


.4142 6172


2.4142 3828


30


40


. 3854 5859


.9228 9651


.4176 6208


2.3945 3792


20


60


.3881 5889


.9216 9646


.4210 6243


2.3750 3757


10


33 00


.3907 9.5919


.9205 9.9640


.4245 9.6279


2.3559 0.3721


6^ 00


10


. 3934 5948


.9194 9635


.4279 6314


2.3369 3686


50


20


.3961 5978


.9182 9629


.4314 6348


2.3183 3652


40


30


.3987 6007


.9171 9624


.4348 6383


2.2998 3617


30


40


.4014 6036


.9159 9618


.4383 6417


2.2817 3583


20


50


.4041 6065


.9147 9613


.4417 6452


2.2637 3548


10


24 00


.4067 9.6093


.9135 9.9607


.4452 9.6486


2.2460 0.3514


66 00


10


.4094 6121


.9124 9602


.4487 6520


2.2286 3480


50


20


.4120 6149


.9112 9596


.4522 6553


2.2113 3447


40


30


.4147 6177


.9100 9590


.4557 6587


2.1943 3413


30


40


.4173 6205


.9088 9584


.4592 6620


2.1775 3380


20


60


.4200 6232


.9075 9579


.4628 6654


2.1609 3346


10


26 00


.4226 9.6259


.9063 9.9573


.4663 9.6687


2.1445 0.3313


65 00


10


.4253 6286


.9051 9567


.4699 6720


2.1283 3280


50


20


.4279 6313


.9038 9561


.4734 6752


2.1123 3248


40


30


.4305 6340


.9026 9555


.4770 6785


2.0965 3215


30


40


.4331 6366


.9013 9549


.4806 6817


2.0809 3183


20


60


.4358 6392


.9001 9543


.4841 6850


2.0655 3150


10


26 00


.4384 9.6418


.8988 9.9537


.4877 9.6882


2.0503 0.3118


64 00


10


.4410 6444


. 8975 9530


.4913 6914


2.0353 3086


50


20


.4436 6470


.8962 9524


.4950 6946


2.0204 3054


40


30


.4462 6495


.8949 9518


.4986 6977


2.0057 3023


30 1


40


.4488 6521


.8936 9512


.5022 7009


1.9912 2991


20


50


.4514 6546


.8923 9505


.5059 7040


1.9768 2960


10


27 00


.4540 9.6570


.8910 9.9499


.5095 9.7072


1.9626 0.2928


63 00


10


.4566 6595


.8897 9492


.5132 7103


1.9486 2897


50


20


.4592 6620


.8884 9486


.5169 7134


1.9347 2866


40


30


.4617 6644


.8870 9479


.5206 7165


1.9210 2835


30


40


.4643 6668


.8857 9473


.5243 7196


1.9074 2804


20


50


.4669 6692


.8843 9466


.5280 7226


1.8940 2774


10


28 00
o /


.4695 9.6716


.8829 9.9459


.5317 9.7257


1.8807 0.2743


62 00

o /


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


Angle


Cosine


Sine


Cotangent


Tangent


Angle



Digitized by VjOOQIC



REFERENCE TABLES



409



TABLE XU.— Continued



Angle


Sine


Cosine


Tangent


Cotangent


Anglb


o /

28 00


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


o /

62 00


.4695 9.6716


.8829 9.9469


.6317 9.7257


1.8807 0.2743


10


.4720 6740


.8816 9453


.5364 7287


1.8676 2713


60


20


.4746 6763


.8802 9446


.5392 7317


1.8546 2683


40


30


.4772 6787


.8788 9439


. 5430 7348


1.8418 2652


30


40


.4797 6810


.8774 9432


.5467 7378


1.8291 2622


20


50


.4823 6833


.8760 9425


. 5505 7408


1.8166 2592


10


29 00


.4848 9.6856


.8746 9.9418


.6643 9.7438


1.8040 0.2562


61 00


10


.4874 6878


.8732 9411


.6581 7467


1.7917 2633


60


20


.4899 6901


.8718 9404


.5619 7497


1.7796 2603


40


30


.4924 6923


.8704 9397


. 5658 7526


1.7676 2474


30


40


.4950 6946


.8689 9390


.5696 7556


1 . 7556 2444


20


60


.4976 6968


.8676 9383


.6736 7685


.6774 9.7614


1.7437 2416


10


30 00


.6000 9.6990


.8660 9.9375


1.7321 0.2386


60 00


10


.6025 7012


.8646 9368


.5812 7644


1.7205 2356


60


20


.5050 7033


.8631 9361


.5851 7673


1.7090 2327


40


30


.5076 7055


.8616 9353


.5890 7701


1.6977 2299


30


40


.6100 7076


.8601 9346


.5930 7730


1.6864 2270


20


60


.6125 7097


.8687 9338


.5969 7769


1.6763 2241


10


31 00


.5160 9.7118


.8672 9.9331


.6009 9.7788


1.6643 0.2212


59 00


10


.5175 7139


.8557 9323


.6048 7816


1.6634 2184


60


20


.5200 7160


.8642 9316


.6088 7846


1.6426 2166


40


30


.5225 7181


.8626 9308


.6128 7873


1.6319 2127


30


40


.5260 7201


.8511 9300


.6168 7902


1.6212 2098


20


60


.6276 7222


.8496 9292


.6208 7930


1.6107 2070


10


32 00


.6299 9.7242


.8480 9.9284


.6249 9.7958


1.6003 0.2042


58 00


10


.6324 7262


.8465 9276


.6289 7986


1.6900 2014


60


20


. 6348 7282


.8450 9268


.6330 8014


1 . 6798 1986


40


30


.6373 7302


.8434 9260


.6371 8042


1.5697 1958


30


40


.5398 7322


.8418 9252


.6412 8070


1 . 5597 1930


20


60


.6422 7342


.8403 9244


.6453 8097


1.5497 1903


10


33 00


.6446 9.7361


.8387 9.9236


.6494 9.8125


1.5399 0.1876


57 00


10


. 5471 7380


.8371 9228


.6536 8153


1 . 5301 1847


60


20


.5495 7400


.8355 9219


.6577 8180


1 . 6204 1820


40


30


.5519 7419


.8339 9211


.6619 8208


1.6108 1792


30


40


.5544 7438


.8323 9203


.6661 8236


1.5013 1765


20


60


.5568 7457


.8307 9194


.6703 8263


1.4919 1737


10


34 00


.6592 9.7476


.8290 9.9186


.6746 9.8290


1.4826 0.1710


56 00


10


.6616 7494


.8274 9177


.6787 8317


1.4733 1683


60


20


.5640 7513


.8258 9169


.6830 8344


1.4641 1656


40


30


.5664 7531


.8241 9160


.6873 8371


1.4560 1629


30


40


.5688 7550


.8225 9151


.6916 8398


1.4460 1602


20


60


.5712 7668


.8208 9142


.6969 8426


1.4370 1675


10


35 00

• o /


.6736 9.7686


.8192 9.9134


.7002 9.8452


1.4281 0.1648


55 00

o /


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


Angle


Cosine


Sine


Cotangent


Tangent


Angle



Digitized by VjOOQIC



410



REFERENCE TABLES



TABLE Xll.— Continued



Anolb


Sine


Cosine


Tangent


Cotangent


Angle


o /

35 00


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


o /

56 00


.5736 9.7586


.8192 9.9134


.7002 9.8452


1.4281 0.1548


10


.5760 7604


.8175 9125


.7046 8479


1.4193 1521


50


20


.5783 7622


.8158 9116


.7089 8506


1.4106 1494


40


30


.5807 7640


.8141 9107


.7133 8533


1.4019 1467


30


40


.5831 7657


.8124 9098


.7177 8559


1.3934 1441


20


50


.5854 7675


. 8107 9089


.7221 8586


1.3848 1414


10


36 00


.5878 9.7692


.8090 9.9080


.7265 9.8613


1.3764 0.1387


54 00


10


.5901 7710


.8073 9070


.7310 8639


1.3680 1361


50


20


. 5925 7727


.8056 9061


.7355 8666


1.3597 1334


40


30


.5948 7744


.8039 9052


.7400 8692


1.3514 1308


30


40


.5972 7761


. 8021 9042


.7445 8718


1.3432 1282


20


50


.5995 7778


.8004 9033


.7490 8745


1.3351 1255


10


37 00


.6018 9.7795


.7986 9.9023


.7536 9.8771


1.3270 0.1229


53 00


10


.6041 7811


. 7969 9014


.7581 8797


1.3190 1203


50


20


.6065 7828


. 7951 9004


.7627 8824


1.3111 1176


40


30


.6088 7844


.7934 8995


. 7673 8850


1.3032 1150


30


40


.6111 7861


.7916 8985


.7720 8876


1.2954 1124


20


50


.6134 7877


. 7898 8975


.7766 8902


1.2876 1098


10


38 00


.6157 9.7893


.7880 9.8965


.7813 9.8928


1.2799 0.1072


52 00


10


.6180 7910


.7862 8955


.7860 8954


1 . 2723 1046


50


20


.6202 7926


. 7844 8945


.7907 8980


1.2647 1020


40


30


.6225 7941


.7826 8935


.7954 9006


1.2572 0994


30


40


.6248 7957


. 7808 8925


.8002 9032


1.2497 0968


20


50


.6271 7973


.7790 8915


.8050 9058


1.2423 0942


10


39 00


.6293 9.7989


.7771 9.8905


.8098 9.9084


1.2349 0.0916


51 00


10


.6316 8004


.7753 8895


.8146 9110


1.2276 0890


50


20


.6338 8020


.7735 8884


.8195 9135


1.2203 0865


40


30


.6361 8035


.7716 8874


.8243 9161


1.2131 0839


30


40


.6383 8050


.7698 8864


.8292 9187


1.2059 0813


20


60


.6406 8066


.7679 8853


.8342 9212


1.1988 0788


10


40 00


.6428 9.8081


.7660 9.8843


.8391 9.9238


1.1918 0.0762


50 00


10


.6450 8096


.7642 8832


.8441 9264


1 . 1847 0736


50


20


.6472 8111


.7623 8821


.8491 9289


1.1778 0711


40


30


.6494 8125


. 7604 8810


.8541 9315


1.1708 0685


30


40


.6517 8140


. 7585 8800


.8591 9341


1 . 1040 0659


20


60


. 6539 8155


.7566 8789


.8642 9366


1.1571 0634


10


41 00


.6561 9.8169


.7547 9.8778


.8693 9.9392


1.1504 0.0608


49 00


10


. 6583 8184


.7528 8767


.8744 9417


1 . 1436 0583


50


20


.6604 S198


.7509 8756


.8796 9443


1.1369 0557


40


30


.6626 8213


.7490 8745


.8847 9468


1.1303 0532


30


40


.6648 8227


.7470 8733


.8899 9494


1 . 1237 0506


20


50


.6670 8241


.7451 8722


.8952 9519


1.1171 0481


10


42 00

o /


.6691 9.8255


.7431 9.8711


.9004 9.9544


1.1106 0.0456


48 00

o /


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


Angle


Cosine


Sine


Cotangent


Tangent


Angle



Digitized by VjOOQIC



EEFEEENCE TABLES



411



TABLE Xll— Continued



Angle


Sine


Cosine


Tangent


Cotangent


Angle


o /

42 00


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


o /

48 00


.6691 9.8255


.7431 9.8711


.9004 9.9544


1.1106 0.0456


10


.6713 8269


.7412 8699


.9057 9570


1.1041 0430


50


20


.6734 8283


. 7392 8688


.9110 9595


1.0977 0405


40


30


.6756 8297


.7373 8676


.9163 9621


1.0913 0379


30


40


.6777 8311


. 7353 8665


.9217 9646


1.0850 0354


20


50


.6799 8324


.7333 8653


.9271 9671


1.0786 0329


10


43 00


.6820 9.8338


.7314 9.8641


.9325 9.9697


1.0724 0.0303


47 00


10


.6841 8351


,7294 8629


.9380 9722


1.0661 0278


50


20


.6862 8365


.7274 8618


.9435 9747


1.0599 0253


40


30


.6884 8378


. 7254 8606


.9490 9772


1.0538 0228


30


40


.6905 8391


.7234 8594


.9545 9798


1.0477 0202


20


50


.6926 8405


.7214 8582


.9601 9823


1.0416 0177


10


44 00


.6947 9.8418


.7193 9.8569


.9657 9.9848


1.0355 0.0152


46 00


10


.6967 8431


.7173 8557


.9713 9874


1.0295 0126


50


. 20


.6988 8444


.7153 8545


.9770 9899


1.0235 0101


40


30


.7009 8457


.7133 8532


.9827 9924


1.0176 0076


30


40


.7030 8469


.7112 8520


.9884 9949


1.0117 0051


20


50


.7050 8482


.7092 8507


.9942 9975


1.0058 0025


10


45 00

o /


.7071 9.8495


,7071 9.8495


1.0000 0.0000


1.0000 0.0000


45 00

o /


Nat. Log.


Nat. Log.


Nat. Log.


Nat. Log.


Angle


Cosine


Sine


Cotangent


Tangent


Angle



Digitized by VjOOQIC



412



REFERENCE TABLES



TABLE XIIL— THREE-PLACE NATURAL TRIGONOMETRIC
FUNCTIONS



Deg.


am


cos


.tan


Deg.


sin


cos


tan





.000


1.000


.000


46


.719


.695


1.04


1


.017


.999


.017


47


.731


.682


1.07


2


.035


.999


.035


48


.743


.669


1.11


3


.052


.999


.052


49


.755


.656


1.15


4


.070


.998


.070


50


.766


.643


1.19


6


.087


.996


.087


51


.777


.629


1.23


6


.105


.995


.105


52


.788


.616


1.28


7


.122


.993


.123


53


.799


.602


1.33


8


.139


.990


.141


54


.809


.588


1.38


9


.156


.988


.158


55


.819


.574


1.43


10


.174


.985


.176


56


.829


.559


1.48


11


.191


.982


.194


57


.839


.545


1.54


12


.208


.978


.213


58


.848


.530


1.60


13


.225


.974


.231


59


.857


.515


1.66 !


14


.242


.970


.249


60


.866


.500


1.73


15


.259


.966


.268


61


.875


.485


1.80


16


.276


.961


.287


62


.883


.469


1.88


17


.292


.956


.306


63


.891


.454


1.96


18


.309


.951


.325


64


.899


.438


2.05


19


.326


.946


.344


65


.906


.423


2.14


20


.342


.940


.364


66


.914


.407


2.25


21


.358


.934


.384


67


.921


.391


2.36


22


.375


.927


.404


68


.927


.375


2.48


23


.391


.921


.424


69


.934


.358


2.61


24


.407


.914


.445


70


.940


.342


2.75


25


.423


.906


.466


71


.946


.326


2.90


26


.438


.899


.488


72


.951


.309


3.08


27


.454


.891


.510


73


.956


.292


3.27


28


.469


.883


.532


74


.961


. .276


3.49


29


.485


.875


.554


75


.966


.259


3.73


30


.500


.866


.577


76


.970


.242


4.01


31


.515


.857


.601


77


.974


.225


4.33


32


.530


.848


.625


78


.978


.208


4.70


33


.545


.839


.649


79


.982


.191


6.14


34


.559


.829


.675


80


.985


.174


5.67


35


.574


.819


.700


81


.988


.156


6.31


36


.588


.809


.727


82


.990


.139


7.12


37


.602


.799


.754


83


.993


.122


8.14


38


.616


.788


.781


84


.995


.105


9.51


39


.629


.777


.810


85


.996


.087


11.4


40


.643


.766


.839


86


.998


.070


14.3


41


.656


.755


.869


87


.999


.052


19.1


42


.669


.743


.900


88


.999


.035


28.6


43


.682


.731


.933


89


.999


.017


57.3


44


.695


.719


.966


90


1.000


.000


Inf.


45


.707


.707


1.000











Digitized by VjOOQIC



GREEK ALPHABET



Aa


Alpha


1 L


Iota


Pp


Rho


B/?


Beta


Kk


Kappa


2(7


Sigma


A^>


Gamma


A A


Lambda


Tt


Tau


AS


Delta


M/x


Mu


Yv


Upsilon


E c


Epsilon


Nv


Nu


4><^


Phi


2^


Zeta


E^


Xi


Xx


Chi


Hr,


Eta


O o


Omicron


^l/r


Psi


0^


Theta


Utt


Pi


O a>


Omega



In the applications of mathematics, angles are commonly
denoted by the small or lower case letters of the Greek alphabet.
Those most generally used are a, 0^ <f>j and 8.

413



Digitized by VjOOQIC



Digitized by VjOOQIC



INDEX



Absolute temperature, 86
Accurate use of tables, 224
Actual weight, 45
Addition, 102-105
Air, resistance, 97

dry volume, 59
Algebraic notation, 11-18
Alphabet, 5
Amperes, 35
Anemometer, 90
Angular velocity, 35, 88
Area, circle, 29

cone, 31

cylinder, 31

ellipse, 30

on a globe, 89

parallelogram, 28

pyramid, regular, 31

regular polygon, 29

ring, 30

ring, cylindrical, 33

sector, 30

sphere, 32

trapezium, 28

trapezoid, 28

triangle, 27, 28
Areal velocity, 87
Armor penetration, 85
Atomic weights, 397
Avoirdupois weight, 394
Axes, ellipse, 30

of reference, 63-64
AxioDas, 10



B

Barometer, 77

Battery, multiple-series, 36

parallel, 36

series, 35
Beam, deflection, 48, 96

rupture, 97

weight, 90
Bending of bar, 89
Binomial formula, 195

theorem, 191-199
Boyle's law, 88-89
Briggs' system, 223



Calorimeter, 56
Center of gravity, 45
Centrifugal force, 34, 89
Charles' law, 86
Check, 40
Circle, arc of sector, 30

area, 29

area sector, 30

ratio circumference to diameter,
29
Coefficient, 16

of friction, 35
Components, 63
Compound motor, 53-54
Cone, area, 31

frustum, 32

volume, 31
Continued proportion, 38

415



Digitized by VjOOQIC



416



INDEX



Convention of signs, 64

Ck)pper wire, resistance, 50

Cosine, 66

Cotangent, definition, 72

Coulomb's law, 98

Cube, diagonal of, d9

Cube root, polynomial, 205-206

Cubic measure, 393

Current, series battery, 35

multiple battery, 36

multiple-series battery, 36

through shunted galvanometer,
36

variation, 98
Cutting speed, 41
Cylinder, area, 31

lateral sin^ace, 99

slide-rule computation, 337-341

volimie, 3.1

weight, 97
Cylindrical ring, area, 33



D

Definition, absolute temperature,
86,92
addition, 102
antilogarithm, 235
areal velocity, 87
checking, 40
coefiScient, 16
complex fraction, 151
compound ratio, 14
cotangent, 72
direct variation, 78
division, 115
equation, 14
expansion, 192
exponent, 16

exponential equation, 252
fraction, 144

fractional, simple equation, 166
factorial, 191
factoring, 14, 128
factors, 128
formula, 350
frustum, 32



Definition, functions of an angle, 66
grouping, 131
"into," 35

inverse variation, 78
involution, 247
"jointly," 90
known quantity, 18
LL scale, 342

least common denominator, 40
like terms, 101
logarithm, 222
members, 15
modulus, 239
molecular weight, 57
multiplication, 113
pitch of screw, 39
polynomial, 139
prime numbers, 144
proportion, 37

continued, 38

extremes, 38

means, 38

simple, 38

terms, 38
pyramid, regular, 31
quadratic equation, 155
radical, 207
radical equation, 219
ratio, 12, 26-27
rational quantity, 208
rationalization; 218
reduction, 208
regular polygon, 29-
resultant, 74
rise of a chord, 47
sector, 30

significant formula, 26
similar radicals, 213
simple equation, 18

fraction, 151
simplest form of, radical, 208

result, 351
simultaneous equations, 173
subtraction, 105
subtrahend, 105
supplement of an angle, 69
surd quantity, 208
table of logarithms, 222



Digitized by VjOOQIC



INDEX



417



Definition, terms, 15
of a fraction, 144

transformation, 350

trapezium, 28

trapezoid, 28

unlike terms, 101

work, 34
Deflection of beam, 48
De Morgan, 60
Density of a gas, 89
Diameter, long piston-rod, 51

pulley arm, 43

shaft, 43 .
Diffusive power, 99
Division, 115-118
Dry air, volume, 59
Dry Measure, 393
Dynamo, resistance of shunt
winding, 52



E

Element, percentage composition,

57
EfiSciency, shunt motor, 52
Electrical, efficiency, 36

transmission, 46
Elevation, outside rail, 48
Ellipse, area, 30

axes, 30

perimeter, 30, 370
Elongation, of a spring, 93

of a wire, 95
Equation, 14-16

quadratic, 155-165

simple, 18-25

simple fractional, 166-172
Equations, simultaneous simple,
173-179

trigonometric, 70-73
Equilibrium on inclined plane, 49

of liquids, 84
Equivalents, U. S. and metric, 396
Examples, addition, 103-105

binomial formula, 197-199

common factor, 129-130

difference of cubes, 123



Examples, division, 117-118
exponents, 184-185, 187-188,

190
factoring, 129-130, 132-134,

135-136, 139, 141-143
factor law, 127
fractions, 145-146, 148-151,

153-154
functions, acute angle, 66

obtuse angle, 70
grouping, 132-133
logarithmic computation, 266-

277
logarithms, 226, 227, 231, 234,

238, 239, 242, 244, 245-246,

248-249, 251-252, 254, 268-

274
multiplication, 114-115
powers, 201

product sum and difference, 122
projection, 62

quadratic, 160-161, 163-165
radicals, 210-217, 219-220
removal of parenthesis, 109-112
resolution, 64-65, 68
resultant, 76
roots, 203-206
simple equations, 19-25
simple fractional equation, -

167-172
simultaneous simple equations,

176-179
slide-rule, 291-202, 294, 299,

304-305, oC7, 311, 315-316,

321-324, 326-328, 332, 335,

338, 341, 346, 349
square of, any polynomial, 125

sum of two numbers, 120-
121
subtraction, 106-108
sum of cubes, 124
trigonometric equations, 70-73
Expansion, 192-197
Exponent, 16-17
Exponents, 180-190
fractional, 185-188
negative, 182-185
zero, 181-182



Digitized by VjOOQIC



418



INDEX



Factor, law, 126

with negative exponent, 183
Factorial B3mibol, 191
Factoring, 128-143

cases, 128

common factor, 129-130

difference of two cubes, 134-135

difference two squares, 133-134

grouping, 131-133

polynomial, 139-140

special expressions, 140-143
methods, 141-143

sum of two cubes, 135-136

trinomial, 136-139
Factors, 14
Falling body, average velocity, 33

change in velocity, 33

final velocity, 33

space traversed, 33
Flow, from orifice, 98

of gas, 87

through a pipe, 87
Flux, 47
Force, 27

centrifugal, 34
Forces, 63-76

Formula, adiabatic expansion, 389
* area, trapezoid, 369
triangle, 369

armatures, winding, 361

attracted disk electrometer, 388

battery, electromotive force of,
360

beams, 356

belt, effective pull, 373

belting, 359

bending moment, 356

bending moment of wall-brack-
et, 381

binomial, 195

boiler, pitch of, 359
plate, 384
stay, diameter, 359


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